curve #6410

y² = x³ − x² − 1901618823663852769630765553180x + 1019010842263780210217390957162115251447040900

a-invariants: [0, -1, 0, -1901618823663852769630765553180, 1019010842263780210217390957162115251447040900]
c-invariants: [91277703535864932942276746552656, -880425367715905553961604571798469923589764021696]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 20677806130408820875829953675519943556998496969903871127353083002520
discriminant (Δ): -8482502432644330619784887388442762223331161679540807018313182068559553270185689330700000000
Faltings height: 16.2623
naive height: 220.7935
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 23, 61, 79, 2446754919520081, 233627663003968707272836898090883125029
regulator: 8920401443822112028.2412409403284513422865123478644738865683267482496774356069821
submitted by: apkorte
submitted at: 2026-11-02 06:24:16 UTC
last updated: 2026-11-02 06:24:16 UTC

(476675600806310, -14861547694426535602500)
(332493732465800, 20578930396779896010870)
(770902549208060, -3344890163441873660250)
(1247484153729810, 24251333644822239910500)
(-1230894719279320, 38662289034097841021910)
(1084063492325810, -15215775939313735831500)
(46122896668628685, -9901088073871038381587250)
(794385665333165, 3112564553245210253190)
(779913283389860, 3210421184661644660850)
(278157197823410, 22618207227539835611700)
(-3174916531592251/4, -360295615217939675551035/8)
(-818082611421440, -45024247410171608193250)
(36782501410560, 30807698878266565505250)
(6041394771306040/9, 181101138173566209849250/27)
(4573150517329540/9, 366186987969942561672250/27)
(18430129162531992, 2495220962993493670477542)
(263333602869060, 23162717153238539399250)
(752579253197040, 3759580195298988614190)
(2875441938641165/4, 38773881567328640125575/8)
(952237058673260, -8465520485077247332650)
(1113875991525202, -16818180724452770675012)

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