curve #6246

y² + xy + y = x³ − x² − 12638985686873919257040169231952x + 17237263575276343178927445047437977419974065715

a-invariants: [1, -1, 1, -12638985686873919257040169231952, 17237263575276343178927445047437977419974065715]
c-invariants: [606671312969948124337928123133681, -14892995729038757776572404156219852970181038676425]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 5382242105315208565538567681079739613194582860098632595611772092362
discriminant (Δ): 858856880063630807524926760289128012441655336568777465610336006526341295110191684765550313472
Faltings height: 16.6907
naive height: 226.4566
primes of bad reduction: 2, 3, 13, 17, 19, 23, 53, 59, 89, 507383, 46550314289, 36232411823483672846478677662909993369
regulator: 7778330271167593497.5009188515337852033735399005052186605702669102022555456126216
submitted by: apkorte
submitted at: 2026-10-31 21:50:44 UTC
last updated: 2026-10-31 21:50:44 UTC

(2232878603373853, 12186481002889483818257)
(2911396518981847, 71539010689844510448695)
(3574564869062045, 133163213959202034062225)
(-15584158874993687/49, -49970811767841856832351809/343)
(1164472831563493, -64019761297073678182111)
(-14283584059314881/4, 1038035288864995451425663/8)
(-2553088264461881, 181284356083446135985895)
(2331558993473525, 21058671165983817982409)
(6413059756581085, 447140637887462163131345)
(2597878334199457, -43996867238877691522123)
(29682164898395701/25, 7811072988388658677576909/125)
(-3960231898657427, 71975911799076035506289)
(2326037876936317, -20577194888143018540303)
(182448476701009957/49, 50641602296733999282043031/343)
(174744044870595337645/73441, 501548257113977910773365253375/19902511)
(2371217055152413, 24496058074820022554897)
(-963008834171933, 168865738634249610220697)
(1908981954489175, -8148811795054807966735)
(317785015731193183/169, 24052897491476986124227955/2197)
(3089306054892301, -87608930638646823882943)
(29477415441192133/9, -2828725456629666054851701/27)

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