curve #5758

y² = x³ − 1133898370046332930775511324675

a-invariants: [0, 0, 0, 0, -1133898370046332930775511324675]
c-invariants: [0, 979688191720031652190041784519200]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 4535593480185331723102045298700
discriminant (Δ): -555433421872491605967622701583087389863015673206042849985630000
Faltings height: 10.7185
naive height: 151.9296
primes of bad reduction: 2, 3, 5, 7, 17, 19, 37, 43, 89, 139, 307
regulator: 10069191152843.0638584757384426922908375229947147460983
submitted by: Maksym Voznyy
submitted at: 2026-10-24 19:40:43 UTC
last updated: 2026-10-24 19:40:43 UTC

(30650672184504612762193424020445599/35394821346683943847609, -5366110675574723575376644621230665042411210308039418/6659008770411094569789935982534227)
(743767802955598030166384117222050684284139/537858798377706931892863870225, 641439895566717728446110585913290377647729825872624859545401912/394459496386971709407103683281552945640421625)
(611428329106629658074511/24092262941769, 461218706660070734982737564514603734/118254150223960716603)
(8067225325410230611963665859239968950399201/232257334038313748349732485515236, -22601099097392451128908869947448556552650059557387362846604179599/3539599744117592829402195099740318975463308922984)
(9124509746245338421705172936839653288218239459969/51732018088933622103326275171096762624, 27559379309630291725626559093236105824321301635336632374096548656735906753/372082402867996041805433325667825720875191680114949869568)
(3615402531583877471029531673998146417151/282580745206417577497424997049, -147212260404198884820532780031336675513605971262903921755374/150215189203475906833944653315020791695093843)
(25518536673042346419040842932248533199/219271026015510417577321225, 128862747060627688782318743894369628059379063002839346582/3246922129663620467919961052546049342875)
(21946301141929000199258491860289870224095641/1098974822927353059966477761496064, -95211430185234594313453363656878034603208695021244241151224297539/36431882663531714643049168202365390798735669952512)

Voznyy (2023), A = 409859663434410, [r, s, t] = [285, 356, 480] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-24 19:40:43 UTC · history