curve #4140

y² + xy = x³ + x² − 398266399363374792852x + 2419040230492410318903123447324

a-invariants: [1, 1, 0, -398266399363374792852, 2419040230492410318903123447324]
c-invariants: [19116787169441990056921, -2090050759288818419303113583914781]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 507140210863489553123473270313412092354332030170894990
discriminant (Δ): 1515015832082420933931635186141130617395630142720649194447542500
Faltings height: 10.8371
naive height: 153.9146
primes of bad reduction: 2, 3, 5, 7, 13, 37, 359, 364447, 473549, 2333905697316397, 34720551874639269071
regulator: 37783871602779151.2986547881306733440826525354030502087896978836781833282
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 01:07:01 UTC
last updated: 2026-10-11 01:07:01 UTC

(-2589030798181/2500, 210296697975396333897/125000)
(31439779373, -4579817925308679)
(-7876086957, -2251050420310719)
(6446976303, 345518285811441)
(-122865349703/9, -62227642182517213/27)
(11015317470607/3969, -288920248792894083968/250047)
(-53343650053/4, 18518869531292733/8)
(556370744646/625, -22454450970257040006/15625)
(25134079570, -2878680794467232)
(1252734992372/289, 4322631852032071878/4913)
(15928580358, 341482990261386)
(460942467485/16, 246672854938317627/64)
(-22311464121, 445284037236648)
(-18411785845, 1873602963607777)
(-17092629682, 2057364127569906)
(-15665245542, 2194029527639286)
(2872142548, 1139671870559806)

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