curve #306

y² + xy + y = x³ − 190635540832861113395418678249957061673x + 990015609814751950477026449045375925435404310567801342428

a-invariants: [1, 0, 1, -190635540832861113395418678249957061673, 990015609814751950477026449045375925435404310567801342428]
c-invariants: [9150505959977333442980096555997938960281, -855373486879945685225876610915170799740659469164577268298429]
rank (lower bound): ≥ 15
torsion subgroup: ℤ/2ℤ
conductor (N): 8754566324589342390719388201154487417353298842735433399274068130
discriminant (Δ): 19979259648527920152721269504654080845418246681580564285588027629322200554647008421994468701299288874082355816250000
Faltings height: 20.9058
naive height: 276.0439
primes of bad reduction: 2, 3, 5, 7, 11, 17, 67, 89, 139, 211, 281, 431, 443, 577, 647, 977, 1613, 3863, 10567, 11923, 15361, 73277
regulator: 866428510109092217761.34350224896176079165781011197887550568733013927
submitted by: 7fff-zip
submitted at: 2026-08-24 00:23:06 UTC
last updated: 2026-08-24 00:23:06 UTC

Witness: 15 independent points log in to add more points →

(17837708368958095959, 57141797046705193682764513570)
(956081964350460535456599/101761, -172632009382274406721081888185640070/32461759)
(96077584492833451732967331/494209, 939430036627449734334500038541246751490/347428927)
(639030603634944592453236/69169, -75765043095954480698300068929327400/18191447)
(1082653439809039496094710079/1229881, 35618947185441406825596754838833242136430/1363938029)
(56365494138847638770252436/4959529, 188540991320680895896156740801329969185/11044871083)
(1002676263871249683499098249/102900736, 7923637758713144491991371818820413148555/1043825065984)
(53322716516802377840040924/5612161, 80274460016606606521432236486281043680/13295209409)
(159224591375723687659087770099/6102578161, 55958147206078755259085116019363670682464530/476727303359159)
(29792196302617801003180869396/2695997929, -2135932881599846774119317288664524139368895/139984300467467)
(3180273811424551677256564/136161, 4839911141809909587350696149464196435/50243409)
(178093629228165652491849124/16641, 2376688227386385696622767827536496138275/2146689)
(108070428084813086799136150339843996/9324850018259169, 16537737834103826933387645130231776084755007451494240/900456594448751456646447)
(19501053265090569386856147055830624607619409/2181775985896731160023616, -1290376184337711601927987569446851062337927913527041811784826485/3222665545741906469079140509853518336)
(38920780690580114070469605263630045173310699548770731618937/4092467494828505665630101150761616668224, -1596470729716437891205709551447684752893494552614575452870062136629917090304257139785591/261804952630804209807466242303354715819258089600597401978368)

Commentary

2-isogeneous to the curve [1, 0, 1, 34318214642441646362435632562579908747, 3184376895814127197244886284686214848599453811643486936756] found by Dujella (2002)

last edited by dujella at 2026-09-23 22:20:34 UTC · history