curve #6152

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y² + xy = x³ − 287690454046158601981875551657963370x + 49010122081886508497565488771865682154437624005615012

a-invariants: [1, 0, 0, -287690454046158601981875551657963370, 49010122081886508497565488771865682154437624005615012]
c-invariants: [13809141794215612895130026479582241761, -42344745478749943362610294990215368724129146860224733009]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 294736122655688545759494666473336277525089326408881751415903698687214680292610
discriminant (Δ): 486238935690146517922721541174559477274003921797914399794230152124190137137468141430213166824919616000000000
Faltings height: 19.3815
naive height: 256.5552
primes of bad reduction: 2, 3, 5, 7, 13, 19, 23, 29, 41, 47, 83, 4278073, 12450399471465570375449578820791216049071073775459542270113
regulator: 4986145782265247346046.15823941520021001735778764015478325301270656319372479530915265
submitted by: Ritik Jain
submitted at: 2026-10-29 13:48:30 UTC
last updated: 2026-10-29 13:48:30 UTC

Witness: 23 independent points log in to add more points →

(2836897221750460479396/6889, -11030443388777399459518747066734/571787)
(-404243930810695372, 315037245170703756330378566)
(47122557215684838223615884170344050337638984/240757585591926684947590681, 52777033230411022351871527779883146970659418142331735295363345578/3735682596120750468373530173886782167421)
(3033504454781388114, 5204907363078623136836608218)
(154371188126029938676/9, 1917074705268341233033690101986/27)
(-8225694517289176728/49, 104361295765026909182207296158/343)
(820283119060357464, -604120687101972802649911482)
(6633641874589922964, 17031011184661506691277956518)
(125718580420138284, -121774747285752755182461522)
(-274594663682709228, 327571878896045636889806118)
(184220708507978628, 47576576373312177423590406)
(483514653163777524, -151481786839597805087692602)
(12139135912953878004/25, -19284541267656140047813377618/125)
(28001089870787680236/49, -91536597486751718719119679326/343)
(29342500850150630964, -158918164394216905939650295482)
(273007671287599608244/1521, 3331756656416547749631425711242/59319)
(5983889074920203730358356/139129, 14636649102977267369222792634205422606/51895117)
(13444556492998109244, 49258164067515109202625889758)
(897216658012758002004/361, -26285443796325032688140342575038/6859)
(4021889120446239396972/1849, 247811407670342211180112387820682/79507)
(412139796680888964, 21146582158250825877952518)
(15818213920864255384/81, -12103373519372882264345067178/729)
(790978297870143075204/361, -21622285204877297457619423700238/6859)

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