curve #1960

y² = x³ + x² − 61440827013714173064683625x + 189790786361878474776598110639658648059

a-invariants

[0, 1, 0, -61440827013714173064683625, 189790786361878474776598110639658648059]

rank (lower bound)

≥ 19

torsion subgroup

trivial

conductor (N)

40084776349308514240515698074406590063523930495828069253489096

discriminant (Δ)

-716868015445302444476613756146679634325827315852813358713637120014625744333568

Faltings height

13.7196

naive height

189.8011

primes of bad reduction

2, 3, 13, 19, 43, 73, 313, 839, 2749, 1146608983164469723271, 35650096999858314311827

regulator

237829970495766684.8779142163629489660288588711877121122992226715846559192474

submitted by

Ritik Jain

submitted at

2026-09-25 20:06:48 UTC

later contributions

(-3269710534171649343970922502363/531137753027488324, -7082014644914695936769992656886089666094184985/387088935743929716129818168)
(15072987432237, -51847860138786228534)
(49659839881551, 345839218774675666794)
(1384871022885717, -51535566116143293024594)
(176873376149811, 2350034693421012512694)
(39767429630963181/9409, 2161732044292319864033526/912673)
(41268063177213453/17956, -18749388752411873847176925/2406104)
(-2644059311371, -18269078444834545458)
(-193113605316661/25, -1783082659569285646338/125)
(84849304199319/25, -563993221935832993278/125)
(9053825870547, 19382319386056953846)
(895435903965222/169, 7920106352746200369405/2197)
(306541441959520639/5625, -168056046469460493800306162/421875)
(-8759307728493, 7477157109227993226)
(-1210801599498, 16199023235555768361)
(-28503631064956419/34225, -98167335544293457686173946/6331625)
(709507456875938373/97969, -342384357984162743578327518/30664297)
(90373582380909199185390717/15326058352201, 342197649188454262686663785579548619994/59999234866172437051)
(154366214051813682448318569/15728648356096, 1438934716448431140310899400067967883317/62378812746781945856)

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