curve #5715

y² = x³ − 982211178304238657825137365498675

a-invariants: [0, 0, 0, 0, -982211178304238657825137365498675]
c-invariants: [0, 848630458054862200360918683790855200]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 6494620852460680104802949110644300
discriminant (Δ): -416767161075465990996156387083809511188290977208450997731976358430000
Faltings height: 11.8458
naive height: 165.4579
primes of bad reduction: 2, 3, 5, 7, 13, 19, 31, 43, 61, 79, 89, 523
regulator: 16128363554293.2203031100004606096041421784096553921348
submitted by: Maksym Voznyy
submitted at: 2026-10-24 15:49:26 UTC
last updated: 2026-10-24 15:49:26 UTC

(809139372134586942957067877898169/2630332148667431487876, -22624637283924918083559133929097105988506101229747/134901223818897622472768905791624)
(335609898865658463424588073055529/423329332808686085604, 6142196057345995643930627080341592476668068841867/8709987729151007352941839863192)
(68520236744837958114683361645319/46312715900558447649, 567103614133915622072782136582766338247358552322/315173993705024375024336361393)
(57757981863009314242826929/12991944460356, -438950539970461288469871884242128980233/46828606339018818504)
(122560987309865602125191079796471/964243455819406049169, 980020591797774623561688319335411582655147533994/29941947882241238997925272698553)
(83654377736736336982033840462411/215365146509391199281, 758687370252284985520595678467520719157653716316/3160553391417129814538242549929)
(7829181420914895889/78747876, -501488510825521694704954087/698808651624)
(1007783550207015515075319817554998774401/10009463062275650717747588484, 6207305183444357512925812384119729072964602020945106211999/1001419795099206707628846154292810072585352)

Voznyy (2023), A = -325697416718121630, [r, s, t] = [92, 212, 233] for S3 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-24 15:49:27 UTC · history