curve #1956

y² + xy = x³ − 3269080460443701044803230660x + 71978041884815981717114026621460954307600

a-invariants: [1, 0, 0, -3269080460443701044803230660, 71978041884815981717114026621460954307600]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 8063611558467458408236373318031709822048927183583704230
discriminant (Δ): -2199443589166737717144016663574216886420540266520642554537558088280382584320000000
Faltings height: 14.5546
naive height: 201.6775
primes of bad reduction: 2, 3, 5, 7, 13, 17, 29, 31, 43, 4494587948564977327650222364359846967542281879
regulator: 951493105600569.08244324159515980061445796787360314085041999383817382934041
submitted by: Ritik Jain
submitted at: 2026-09-25 20:06:37 UTC
last updated: 2026-09-25 20:06:37 UTC

(1425950537778029260152651151950/43528362518361361, 58586915839733745275776609985334675277112040/9081518976875951220420359)
(783463664740960/9, 18053151499695264376340/27)
(6280487638582917099102/186295201, 23378277177537397384052781485418/2542743198449)
(-1375485379198644/25, -36505493172759873026436/125)
(332319544048177224/9025, -33531100411045326740682108/857375)
(-945834331902096/25, -47021443816189218142452/125)
(16081982618487450, 2039419839828973283412990)
(34031206966812, -11815822989747653844)
(2036275272095820, -91851302599246572955860)
(30608474199388505/64, 5318406005235866315983105/512)
(23754580769671080/529, 1525889638020255961458180/12167)
(2692942130286815820/160801, -9548342986706788411776691860/64481201)
(480445009956765/16, 1909162924472345054835/64)
(3520307859916680/169, -249730036734578588521620/2197)
(-812946246249963/16, -20926131236772908187027/64)
(205608951481416, 2844635669207350065852)
(95882480193530345731080/4787671249, 39946537701664665227540650863306780/331273336732057)
(-159716272120668611989032/61188453769, 4294218710674318037977802337362127204/15135759489661147)

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