Discriminant = -4
List of Kolyvagin primes for -4 : [59, 83, 107, 227, 263, 347, 479, 491]
59
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_59=0

83
The reduction mod 83 map is surjective.
The Kolyvagin class tau_83 is a multiple of 1*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

107
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_107=0

227
The reduction mod 227 map is surjective.
The Kolyvagin class tau_227 is a multiple of 1*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

263
The reduction mod 263 map is surjective.
The Kolyvagin class tau_263 is a multiple of 2*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

347
The reduction mod 347 map is surjective.
The Kolyvagin class tau_347 is a multiple of 2*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

479
The reduction mod 479 map is surjective.
The Kolyvagin class tau_479 is a multiple of 1*(-1 : 1 : 1) + 0*(0 : -1 : 1) in E(Q)/3E(Q).

491
The reduction mod 491 map is surjective.
The Kolyvagin class tau_491 is a multiple of 1*(-1 : 1 : 1) + 0*(0 : -1 : 1) in E(Q)/3E(Q).

Discriminant = -7
List of Kolyvagin primes for -7 : [5, 17, 41, 59, 83, 173, 227, 269, 479]
5
The reduction mod 5 map is surjective.
The Kolyvagin class tau_5 is a multiple of 2*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

17
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_17=0

41
The reduction mod 41 map is surjective.
The Kolyvagin class tau_41 is a multiple of 1*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

59
The reduction mod 59 map is surjective.
The Kolyvagin class tau_59 is a multiple of 0*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

83
The reduction mod 83 map is surjective.
The Kolyvagin class tau_83 is a multiple of 1*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

173
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_173=0

227
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_227=0

269
The part of the map coming from E/QQ is not surjective.
Therefore tau_ 269 =0

479
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_479=0

Discriminant = -11
List of Kolyvagin primes for -11 : [17, 29, 41, 83, 107, 173, 227, 233, 263, 281, 347, 479, 491]
17
The reduction mod 17 map is surjective.
The Kolyvagin class tau_17 is a multiple of 1*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

29
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_29=0

41
The reduction mod 41 map is surjective.
The Kolyvagin class tau_41 is a multiple of 1*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

83
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_83=0

107
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_107=0

173
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_173=0

227
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_227=0

233
The reduction mod 233 map is surjective.
The Kolyvagin class tau_233 is a multiple of 1*(-1 : 1 : 1) + 0*(0 : -1 : 1) in E(Q)/3E(Q).

263
The reduction mod 263 map is surjective.
The Kolyvagin class tau_263 is a multiple of 2*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

281
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_281=0

347
The reduction mod 347 map is surjective.
The Kolyvagin class tau_347 is a multiple of 2*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

479
The reduction mod 479 map is surjective.
The Kolyvagin class tau_479 is a multiple of 1*(-1 : 1 : 1) + 0*(0 : -1 : 1) in E(Q)/3E(Q).

491
The reduction mod 491 map is surjective.
The Kolyvagin class tau_491 is a multiple of 1*(-1 : 1 : 1) + 0*(0 : -1 : 1) in E(Q)/3E(Q).

Discriminant = -19
List of Kolyvagin primes for -19 : [29, 41, 53, 59, 107, 113, 173, 227, 269, 281, 449]
29
The reduction mod 29 map is surjective.
The Kolyvagin class tau_29 is a multiple of 1*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

41
The reduction mod 41 map is surjective.
The Kolyvagin class tau_41 is a multiple of 1*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

53
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_53=0

59
The reduction mod 59 map is surjective.
The Kolyvagin class tau_59 is a multiple of 0*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

107
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_107=0

113
The reduction mod 113 map is surjective.
The Kolyvagin class tau_113 is a multiple of 2*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

173
The reduction mod 173 map is surjective.
The Kolyvagin class tau_173 is a multiple of 1*(-1 : 1 : 1) + 0*(0 : -1 : 1) in E(Q)/3E(Q).

227
The reduction mod 227 map is surjective.
The Kolyvagin class tau_227 is a multiple of 1*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

269
The part of the map coming from E/QQ is not surjective.
Therefore tau_ 269 =0

281
The reduction mod 281 map is surjective.
The Kolyvagin class tau_281 is a multiple of 1*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

449
The reduction mod 449 map is surjective.
The Kolyvagin class tau_449 is a multiple of 0*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

Discriminant = -20
List of Kolyvagin primes for -20 : [17, 53, 59, 113, 173, 233, 479, 491]
17
The reduction mod 17 map is surjective.
The Kolyvagin class tau_17 is a multiple of 1*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

53
The reduction mod 53 map is surjective.
The Kolyvagin class tau_53 is a multiple of 1*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

59
The reduction mod 59 map is surjective.
The Kolyvagin class tau_59 is a multiple of 0*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

113
The reduction mod 113 map is surjective.
The Kolyvagin class tau_113 is a multiple of 2*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

173
The reduction mod 173 map is surjective.
The Kolyvagin class tau_173 is a multiple of 1*(-1 : 1 : 1) + 0*(0 : -1 : 1) in E(Q)/3E(Q).

233
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_233=0

479
The reduction mod 479 map is surjective.
The Kolyvagin class tau_479 is a multiple of 1*(-1 : 1 : 1) + 0*(0 : -1 : 1) in E(Q)/3E(Q).

491
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_491=0

Discriminant = -35
List of Kolyvagin primes for -35 : [41, 53, 59, 107, 113, 233, 263, 269, 347, 479]
41
The reduction mod 41 map is surjective.
The Kolyvagin class tau_41 is a multiple of 1*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

53
The reduction mod 53 map is surjective.
The Kolyvagin class tau_53 is a multiple of 1*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

59
The reduction mod 59 map is surjective.
The Kolyvagin class tau_59 is a multiple of 0*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

107
The reduction mod 107 map is surjective.
The Kolyvagin class tau_107 is a multiple of 2*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

113
The reduction mod 113 map is surjective.
The Kolyvagin class tau_113 is a multiple of 2*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

233
The reduction mod 233 map is surjective.
The Kolyvagin class tau_233 is a multiple of 1*(-1 : 1 : 1) + 0*(0 : -1 : 1) in E(Q)/3E(Q).

263
The reduction mod 263 map is surjective.
The Kolyvagin class tau_263 is a multiple of 2*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

269
The part of the map coming from E/QQ is not surjective.
Therefore tau_ 269 =0

347
The reduction mod 347 map is surjective.
The Kolyvagin class tau_347 is a multiple of 2*(-1 : 1 : 1) + 1*(0 : -1 : 1) in E(Q)/3E(Q).

479
The part of the reduction map coming from the twist is not surjective (i.e., it is zero).
Therefore tau_479=0