curve #5754

y² = x³ − 146117174476027830880061488122675

a-invariants: [0, 0, 0, 0, -146117174476027830880061488122675]
c-invariants: [0, 126245238747288045880373125737991200]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 194822899301370441173415317496900
discriminant (Δ): -9223298788402638293914741372048552750829451777829203401406835230000
Faltings height: 11.5282
naive height: 161.6471
primes of bad reduction: 2, 3, 5, 7, 19, 37, 67, 89, 97, 223, 733
regulator: 58933695233388.3555810555843508224522206702235742579261
submitted by: Maksym Voznyy
submitted at: 2026-10-24 19:22:11 UTC
last updated: 2026-10-24 19:22:11 UTC

(1195941506319439225039/12674481561, -37590200529486905625421118416262/1426905808618941)
(1936661158493005328391953822422119055467530329/23197770497699947842734628776484, 85227640175169685566932363092781605502611421538522124011716383153283/111729890020505886338267117982599803174622381352)
(50719234469809263092750117194850311/132959232779373953223489, 11407400258464132862819754358292921495688266562583466/48481690038197189288138720279935263)
(39261287198797149096216268530656333572921124931841/740128966963990177451393491250818646016, 35750668960147605905852388730793938349939621315227924473845871973224067711/20135439003277003832523697704415093622498964543869011623936)
(112029030885699489449577519586639598012965651/580275882124385150471235255269001, 1173657044461617115629260560756742944008833574038278003203581381924/13978217078510912496027395401030800544313356721499)
(4029515747466291766233697205428852949978004014539/56268529356495871603765454488284760641, 6276608141765989438346757370968811477250972007946259511928546483191638512/422083472426488788445753083404857750158866489382056670561)
(42218649867101069209601566369/287999574324422724, -8471169721133255358136644074984385489598703/154556675942682306768280632)
(64065045273667842532538784966116343525610634624123119/42696947135968741924193069536812878252025, 16215200137253326192659293565894458260905632465986279310751538610571867789870278/8822572494713895701109812902765429183533172591726623969466125)

Voznyy (2023), A = -4652632460367290, [r, s, t] = [9, 99, 169] for S3 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-24 19:22:11 UTC · history