curve #297

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y² + xy + y = x³ − x² − 102056804118937439750571852774621992x + 12353237625156568163254531376811881758355861766631659

a-invariants: [1, -1, 1, -102056804118937439750571852774621992, 12353237625156568163254531376811881758355861766631659]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 4364964377077049758085830839555594579925031504595053979466232451712234336710
naive height: 253.4461
Faltings height: 19.0054
discriminant (Δ): 2106574010048030551500005492957851215353050181457044848295738692839352524513682811850961445705934581760000
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 163, 1021, 217859558691071058451, 70333227941934431744712601307508168934089337
regulator: 17689615308679714285.41047217581495067519854555142043625122536161711342194462
submitted by: 7fff-zip
submitted at: 2026-08-23 15:37:20 UTC
last updated: 2026-08-23 15:37:20 UTC

Witness: 19 independent points

(134683847380952117, -32418581154752223023813559)
(941606153428183283375501117/237190801, 28802904887079577844389321535454578631441/3652975526201)
(429343953146034110891/2809, -2684089699847917842999072927411/148877)
(-18324157075973570778394123/496888681, -1403951782161533459832187054183986478989/11076145588171)
(-127053591551775410347/361, 469065966279772288724294653107/6859)
(18235485702934364373136187/133841761, 48411421011678560383263677947855144419/1548415333009)
(-78076007325281959399/1849, -10239873415122470364142084983849/79507)
(-18170518895108279590461627/158432569, 299457334529853436822905580233703096923/1994190746003)
(-84619536849115479659/1089, 5058607373755602967875039226241/35937)
(463039868947158731490668357/2917188121, 1949207268844319578634982669607975104171/157560247603331)
(266187079526166211301/1849, 2018488057062056778034433443899/79507)
(980586956538421337, 924749597478638770681316421)
(214012919127202413533/289, 2876816705672397467412722451033/4913)
(1128687184987475072126174861/82864609, -37908968735902593136450866956499307454889/754316535727)
(220806894326516499041/625, -2231332394821214542131388440039/15625)
(7258104227033521197, 19535329623898548572548973561)
(143574024578136657680933/375769, 39319498593859689558293016538417077/230346397)
(632253320714231402839429143857/3108253624576, 17419023455485411618215677714548897853466849/5479925738214477824)
(3384115290681731151274637/13535041, 2472921960467755831842685111330944999/49795415839)

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