curve #321

y² + xy + y = x³ − x² − 252160457594955208636121130356708x + 1519947879571352753434584073837249656547139834631

a-invariants: [1, -1, 1, -252160457594955208636121130356708, 1519947879571352753434584073837249656547139834631]
c-invariants: [12103701964557850014533814257121969, -1313234967949648724500821799285058637854564660072553]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 145323169645687309832774307428274845395550177606625215132204062998090
discriminant (Δ): 28125827761934551809384716578000784724253832319205394863425935853850554475927498687104530418892800
Faltings height: 17.4991
naive height: 235.4365
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 31, 47, 397763, 13949939, 15361358835391, 683626354372305968145666651662381
regulator: 1068347134712448769.822543710338758147429771077687677966932786376240443941841
submitted by: Andrii Prokhorenkov
submitted at: 2026-08-24 13:27:05 UTC
last updated: 2026-08-24 19:08:27 UTC

(8085361818428165, 98510473145628176045277)
(10286971323338981, 120690050137716835708797)
(10098758315096645, -57977721275633475876003)
(7356189915620817, -251151488895737428421559)
(6576573337524461, -382153892021529127302939)
(163695487270976429/25, -48344070147563534306722743/125)
(10599968119386917, -195090553020967973011779)
(8128347151095365, -85675330272819793998243)
(1806757901464325, 1034530285796591406389277)
(-17777140938502675, 620151584693996226404397)
(-522465827667794899/841, -31577503379872128964482596847/24389)
(12182460572676665, 506004535155095919135057)
(10155374185699013, -80649360960052087822755)
(87104676516970383, -25306883364704377703800669)
(132858997910662229/625, 18920801656986355323050864133/15625)
(15243321657217925, 1103678244453900258275997)
(-907028931809275, -1322088686443394662951203)
(5392174731437765, 563058669993768872216157)
(68036049746118725, -17300181931409201573135523)

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