Magma V2.21-1 Wed Jan 8 2020 09:19:48 on sequoia [Seed = 2767153708]
Type ? for help. Type -D to quit.
We check assertions in Theorem 3.
Computing forms at level N1=I2*I3*I7...
Done !
We first perform standard elimination at level N1 = I2*I3*I7 using primes q =
13, 29 and 41 :
Performing standard elimination for 5 form(s) with set of auxiliary primes [ 13,
29, 41 ]
Checking form no 1
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 1 is eliminated
*************************************************************
Checking form no 2
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 2 is eliminated
*************************************************************
Checking form no 3
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Form no 3
with coefficient field : Number Field with defining polynomial x^3 - 3*x^2 -
10*x - 1 over the Rational Field
is not eliminated for prime(s) : { 5, 13 }
*************************************************************
Checking form no 4
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Form no 4
with coefficient field : Number Field with defining polynomial x^3 - x^2 - 30*x
- 27 over the Rational Field
is not eliminated for prime(s) : { 11 }
*************************************************************
Checking form no 5
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Form no 5 is eliminated
*************************************************************
*************************************************************
The prime p = 11 survives for the form no 4 ; we discard it using refined
elimination with q = 5 :
Performing refined elimination with set of auxiliary primes [ 5 ]
Dealing with q = 5
This form can be eliminated for large enough p !
The form with coefficient field : Number Field with defining polynomial x^3 -
x^2 - 30*x - 27 over the Rational Field
is not eliminated for 6 prime ideal(s) above : { 13, 67, 125, 205379 }
*************************************************************
*************************************************************
The primes p = 5, 13 survive for the form no 3 ; we discard p = 5 using refined
elimination with q = 29 :
Performing refined elimination with set of auxiliary primes [ 29 ]
Dealing with q = 29
This form can be eliminated for large enough p !
The form with coefficient field : Number Field with defining polynomial x^3 -
3*x^2 - 10*x - 1 over the Rational Field
is not eliminated for 2 prime ideal(s) above : { 13, 24389 }
*************************************************************
*************************************************************
For each form f at level N1, we compute Norm(a_Q(f)-(Norm(Q)+1)) mod 13 for any
of the three prime ideals Q above 29 in K :
Form no 1 : Norm(a_Q(f)-(Norm(Q)+1)) mod 13 = 7
Form no 2 : Norm(a_Q(f)-(Norm(Q)+1)) mod 13 = 12
Form no 3 : Norm(a_Q(f)-(Norm(Q)+1)) mod 13 = 0
Form no 4 : Norm(a_Q(f)-(Norm(Q)+1)) mod 13 = 8
Form no 5 : Norm(a_Q(f)-(Norm(Q)+1)) mod 13 = 12
Hence form no 3 is the unique form with reducible mod 13 representation whose
existence is predicted by Martin's result.
It has exactly 1 prime ideal above 13 in its coefficient field.
*************************************************************
Computing forms at level N2=I2^3*I3*I7...
Done !
*************************************************************
We first perform standard elimination at level N2 = I2^3*I3*I7 using primes q =
13, 29, 41 and 43 :
Performing standard elimination for 121 form(s) with set of auxiliary primes [
13, 29, 41, 43 ]
Checking form no 1
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 1 is eliminated
*************************************************************
Checking form no 2
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Form no 2 is eliminated
*************************************************************
Checking form no 3
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 3 is eliminated
*************************************************************
Checking form no 4
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 4 is eliminated
*************************************************************
Checking form no 5
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 5 is eliminated
*************************************************************
Checking form no 6
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 6 is eliminated
*************************************************************
Checking form no 7
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 7 is eliminated
*************************************************************
Checking form no 8
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 8 is eliminated
*************************************************************
Checking form no 9
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 9 is eliminated
*************************************************************
Checking form no 10
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 10 is eliminated
*************************************************************
Checking form no 11
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 11 is eliminated
*************************************************************
Checking form no 12
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 12 is eliminated
*************************************************************
Checking form no 13
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 13 is eliminated
*************************************************************
Checking form no 14
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 14 is eliminated
*************************************************************
Checking form no 15
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Form no 15 is eliminated
*************************************************************
Checking form no 16
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 16 is eliminated
*************************************************************
Checking form no 17
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 17 is eliminated
*************************************************************
Checking form no 18
Dealing with q = 13
Dealing with q = 29
Dealing with q = 41
This form can be eliminated for large enough p !
Dealing with q = 43
Form no 18 is eliminated
*************************************************************
Checking form no 19
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 19 is eliminated
*************************************************************
Checking form no 20
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 20 is eliminated
*************************************************************
Checking form no 21
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 21 is eliminated
*************************************************************
Checking form no 22
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Form no 22 is eliminated
*************************************************************
Checking form no 23
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 23 is eliminated
*************************************************************
Checking form no 24
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 24 is eliminated
*************************************************************
Checking form no 25
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 25 is eliminated
*************************************************************
Checking form no 26
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 26 is eliminated
*************************************************************
Checking form no 27
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 27 is eliminated
*************************************************************
Checking form no 28
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 28 is eliminated
*************************************************************
Checking form no 29
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 29 is eliminated
*************************************************************
Checking form no 30
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 30 is eliminated
*************************************************************
Checking form no 31
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 31 is eliminated
*************************************************************
Checking form no 32
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 32 is eliminated
*************************************************************
Checking form no 33
Dealing with q = 13
Dealing with q = 29
This form can be eliminated for large enough p !
Dealing with q = 41
Form no 33 is eliminated
*************************************************************
Checking form no 34
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 34 is eliminated
*************************************************************
Checking form no 35
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 35 is eliminated
*************************************************************
Checking form no 36
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 36 is eliminated
*************************************************************
Checking form no 37
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Form no 37 is eliminated
*************************************************************
Checking form no 38
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Form no 38 is eliminated
*************************************************************
Checking form no 39
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 39 is eliminated
*************************************************************
Checking form no 40
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 40 is eliminated
*************************************************************
Checking form no 41
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 41 is eliminated
*************************************************************
Checking form no 42
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 42 is eliminated
*************************************************************
Checking form no 43
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 43 is eliminated
*************************************************************
Checking form no 44
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 44 is eliminated
*************************************************************
Checking form no 45
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 45 is eliminated
*************************************************************
Checking form no 46
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 46 is eliminated
*************************************************************
Checking form no 47
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 47 is eliminated
*************************************************************
Checking form no 48
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 48 is eliminated
*************************************************************
Checking form no 49
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 49 is eliminated
*************************************************************
Checking form no 50
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 50 is eliminated
*************************************************************
Checking form no 51
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 51 is eliminated
*************************************************************
Checking form no 52
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 52 is eliminated
*************************************************************
Checking form no 53
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 53 is eliminated
*************************************************************
Checking form no 54
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 54 is eliminated
*************************************************************
Checking form no 55
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 55 is eliminated
*************************************************************
Checking form no 56
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Dealing with q = 43
Form no 56
with coefficient field : Rational Field
is not eliminated for prime(s) : { 5 }
*************************************************************
Checking form no 57
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 57 is eliminated
*************************************************************
Checking form no 58
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 58 is eliminated
*************************************************************
Checking form no 59
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 59 is eliminated
*************************************************************
Checking form no 60
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 60 is eliminated
*************************************************************
Checking form no 61
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 61 is eliminated
*************************************************************
Checking form no 62
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 62 is eliminated
*************************************************************
Checking form no 63
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 63 is eliminated
*************************************************************
Checking form no 64
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 64 is eliminated
*************************************************************
Checking form no 65
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 65 is eliminated
*************************************************************
Checking form no 66
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 66 is eliminated
*************************************************************
Checking form no 67
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 67 is eliminated
*************************************************************
Checking form no 68
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 68 is eliminated
*************************************************************
Checking form no 69
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 69 is eliminated
*************************************************************
Checking form no 70
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 70 is eliminated
*************************************************************
Checking form no 71
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 71 is eliminated
*************************************************************
Checking form no 72
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 72 is eliminated
*************************************************************
Checking form no 73
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 73 is eliminated
*************************************************************
Checking form no 74
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 74 is eliminated
*************************************************************
Checking form no 75
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 75 is eliminated
*************************************************************
Checking form no 76
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 76 is eliminated
*************************************************************
Checking form no 77
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 77 is eliminated
*************************************************************
Checking form no 78
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 78 is eliminated
*************************************************************
Checking form no 79
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 79 is eliminated
*************************************************************
Checking form no 80
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 80 is eliminated
*************************************************************
Checking form no 81
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 81 is eliminated
*************************************************************
Checking form no 82
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 82 is eliminated
*************************************************************
Checking form no 83
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 83 is eliminated
*************************************************************
Checking form no 84
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Dealing with q = 43
Form no 84
with coefficient field : Number Field with defining polynomial x^11 - 3*x^10 -
62*x^9 + 53*x^8 + 1431*x^7 + 1540*x^6 - 10083*x^5 - 27056*x^4 - 20844*x^3 -
3040*x^2 + 784*x - 32 over the Rational Field
is not eliminated for prime(s) : { 5 }
*************************************************************
Checking form no 85
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 85 is eliminated
*************************************************************
Checking form no 86
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 86 is eliminated
*************************************************************
Checking form no 87
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 87 is eliminated
*************************************************************
Checking form no 88
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 88 is eliminated
*************************************************************
Checking form no 89
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 89 is eliminated
*************************************************************
Checking form no 90
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Dealing with q = 43
Form no 90 is eliminated
*************************************************************
Checking form no 91
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 91 is eliminated
*************************************************************
Checking form no 92
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 92 is eliminated
*************************************************************
Checking form no 93
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 93 is eliminated
*************************************************************
Checking form no 94
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 94 is eliminated
*************************************************************
Checking form no 95
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 95 is eliminated
*************************************************************
Checking form no 96
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Dealing with q = 43
Form no 96 is eliminated
*************************************************************
Checking form no 97
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Dealing with q = 43
Form no 97 is eliminated
*************************************************************
Checking form no 98
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Form no 98 is eliminated
*************************************************************
Checking form no 99
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 99 is eliminated
*************************************************************
Checking form no 100
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Form no 100 is eliminated
*************************************************************
Checking form no 101
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 101 is eliminated
*************************************************************
Checking form no 102
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 102 is eliminated
*************************************************************
Checking form no 103
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 103 is eliminated
*************************************************************
Checking form no 104
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 104 is eliminated
*************************************************************
Checking form no 105
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 105 is eliminated
*************************************************************
Checking form no 106
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Form no 106 is eliminated
*************************************************************
Checking form no 107
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 107 is eliminated
*************************************************************
Checking form no 108
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Form no 108 is eliminated
*************************************************************
Checking form no 109
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 109 is eliminated
*************************************************************
Checking form no 110
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Form no 110 is eliminated
*************************************************************
Checking form no 111
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Form no 111 is eliminated
*************************************************************
Checking form no 112
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Form no 112 is eliminated
*************************************************************
Checking form no 113
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 113 is eliminated
*************************************************************
Checking form no 114
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 114 is eliminated
*************************************************************
Checking form no 115
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 115 is eliminated
*************************************************************
Checking form no 116
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 116 is eliminated
*************************************************************
Checking form no 117
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 117 is eliminated
*************************************************************
Checking form no 118
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 118 is eliminated
*************************************************************
Checking form no 119
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Form no 119 is eliminated
*************************************************************
Checking form no 120
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Dealing with q = 43
Form no 120
with coefficient field : Number Field with defining polynomial x^18 + 6*x^17 -
129*x^16 - 792*x^15 + 6299*x^14 + 39175*x^13 - 151912*x^12 - 923664*x^11 +
2090978*x^10 + 11261011*x^9 - 17937590*x^8 - 71376648*x^7 + 91261904*x^6 +
219795072*x^5 - 221354112*x^4 - 308115584*x^3 + 219618048*x^2 + 138201344*x
- 84347392 over the Rational Field
is not eliminated for prime(s) : { 5 }
*************************************************************
Checking form no 121
Dealing with q = 13
This form can be eliminated for large enough p !
Dealing with q = 29
Dealing with q = 41
Dealing with q = 43
Form no 121
with coefficient field : Number Field with defining polynomial x^18 - 149*x^16 +
66*x^15 + 8789*x^14 - 7971*x^13 - 261084*x^12 + 353462*x^11 + 4091944*x^10 -
7154721*x^9 - 32293194*x^8 + 66417652*x^7 + 111002728*x^6 - 243935776*x^5 -
155653920*x^4 + 286956800*x^3 + 99560704*x^2 + 9035264*x + 157184 over the
Rational Field
is not eliminated for prime(s) : { 17 }
*************************************************************
*************************************************************
The prime p = 17 survives for the form no 121 ; we discard it using refined
elimination with q = 5 :
Performing refined elimination with set of auxiliary primes [ 5 ]
Dealing with q = 5
This form can be eliminated for large enough p !
The form with coefficient field : Number Field with defining polynomial x^18 -
149*x^16 + 66*x^15 + 8789*x^14 - 7971*x^13 - 261084*x^12 + 353462*x^11 +
4091944*x^10 - 7154721*x^9 - 32293194*x^8 + 66417652*x^7 + 111002728*x^6 -
243935776*x^5 - 155653920*x^4 + 286956800*x^3 + 99560704*x^2 + 9035264*x +
157184 over the Rational Field
is not eliminated for 18 prime ideal(s) above : { 67, 125, 127, 148877,
51895117, 1058089859, 39547260143, 840430616453, 6814692748079 }
*************************************************************
*************************************************************
The prime p = 5 survives for three forms no 56, 84 and 120 ; we discard it using
refined elimination with q = 29, 41, 83 :
Performing refined elimination with set of auxiliary primes [ 29, 41, 83 ]
Dealing with q = 29
This form can be eliminated for large enough p !
Dealing with q = 41
Dealing with q = 83
The form is eliminated
*************************************************************
Performing refined elimination with set of auxiliary primes [ 29, 41, 83 ]
Dealing with q = 29
This form can be eliminated for large enough p !
Dealing with q = 41
The form is eliminated
*************************************************************
Performing refined elimination with set of auxiliary primes [ 29, 41, 83 ]
Dealing with q = 29
This form can be eliminated for large enough p !
Dealing with q = 41
The form is eliminated
*************************************************************
Total time: 22636.150 seconds, Total memory usage: 24059.66MB