curve #2033

y² + xy = x³ − 2169804093800933365192291537396090x − 38883273408123992218250950540971569700398004497500

a-invariants: [1, 0, 0, -2169804093800933365192291537396090, -38883273408123992218250950540971569700398004497500]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 59581557002530875732300241072530
discriminant (Δ): 650260669135709618982645009427312607974621704366998887920452078107108038431525075479966257501441600
Faltings height: 17.9063
naive height: 241.8934
primes of bad reduction: 2, 3, 5, 7, 13, 19, 23, 31, 107, 163, 563, 887, 1621, 1823, 6701, 9341
regulator: 203367184191.95135492731657200855887559120525415013388617
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:05:02 UTC
last updated: 2026-09-26 05:05:02 UTC

(-3218671840802764000/121, -148497103686576181600795250/1331)
(-26843876451231328, 138388149776194963713722)
(-26530909067977750, 93717884502912609946250)
(-245172103847410136/9, 2639226253997923201576514/27)
(-7775259687112057083898/292681, 16383775327666675898748228770162/158340421)
(19843972397623100008/289, 57266638329669335108262087686/4913)
(-2130086281740485182658795710/79697242249, 2943959865489976945466846503357017270860/22499089367588443)
(31151293919806847822984177/219750976, -162949768733096607821801446144585598851/3257588468224)
(2980346680685942157810533/1926544, 5142815292464544073768687723104580609/2674043072)

2-isogenous partner of curve#1827 (Klagsbrun (2020)). Isogenous to curve#2098, curve#2099 (also ours).

last edited by Steps Unbounded at 2026-09-26 21:45:11 UTC · history