curve #4625

y² + xy + y = x³ + x² − 96180274396179737658607503195684835745x + 440507530260581919989915680206240915688210909399060173407

a-invariants: [1, 1, 1, -96180274396179737658607503195684835745, 440507530260581919989915680206240915688210909399060173407]
c-invariants: [4616653171016627407613160153392872115761, -380598506145142778905912046480816856711712926871234530692009]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 12282023191585328240966136440298451368031941176317794532149510
discriminant (Δ): -26885560091168214291089140203663319366248180009176431184703519185121857412400451031831415026533057698571811456000000
Faltings height: 20.8649
naive height: 274.3782
primes of bad reduction: 2, 3, 5, 7, 11, 37, 53, 97, 151, 163, 179, 229, 257, 269, 313, 379, 433, 449, 577, 821, 3529, 4409, 6257, 11489, 32793913
regulator: 373449862155065795.143241061690788885379390735607592506269975819676760543
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:31:11 UTC
last updated: 2026-10-19 03:31:11 UTC

(-2387897561842820513, 25623431666677669707607073696)
(17786911184414741917, 66008162342314635286893467336)
(-14342327137233212917337/1369, 874803338986233048695591213012768/50653)
(4947507110437182377, 9260624166120572128071526256)
(55003434998398568455/9, 242953248457601493748971385216/27)
(14884042998148617995, 48023834974221609222235555496)
(189474566094183365923/9, 2376396797842497294403040950852/27)
(-17274898550331043506337/1849, -1819271657412403109323552702261688/79507)
(-5386083352250219543399653/4541161, 227551310925109871940005720018169349256/9677214091)
(132358940548975107915798953/29626249, 1612415656097276814282438411769069295882/161255673307)
(-17846572421829139464857/7569, 16842466314297220560645649325703728/658503)
(-87162793560448278977/9, 581355458054590263670834017752/27)
(43631413920565582423/9, 253527383211355938171282436352/27)
(-49798129060478756046863121311414603193/4522471542448136281, 123344965776184985913044480246571054258686097869645076896/9617534749048427071351881821)
(75059026906073828538286617273111727/19291301283410641, 29979493259309358510763907615396869906987047228525664/2679429197734619720385689)
(31800148077810394440136562649927832191/15543079911898977025, -973325432113283472631297519159593069850936538950109254496/61278146388552845860926997375)
(190858448522041217321901256872278489/66286118633262649, 233652851896309764965639054221490094913123606953812762/17066084224829401980762643)

X400, T=-1259/5670

last edited by Andrii Prokhorenkov at 2026-10-19 03:31:11 UTC · history