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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(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)/ 3 E(Q).

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