curve #5597

y² + y = x³ + 1421783459238899

a-invariants: [0, 0, 1, 0, 1421783459238899]
c-invariants: [0, -1228420908782408952]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 2362735866713806045837778481
discriminant (Δ): -873274264545022855959780439913043
Faltings height: 4.9997
naive height: 83.3045
primes of bad reduction: 3, 13, 1367, 2843, 320699
regulator: 2014907839828982.293104059334974737176422082525508309362634
submitted by: jesper-petersen
submitted at: 2026-10-23 21:41:37 UTC
last updated: 2026-10-23 21:41:37 UTC

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(-598490084319/13542400, 1821211325555985329/49836032000)
(331612860509193/868716676, 6115440500537952614063/25604555308424)
(-618608332857551/7131802500, 16703710118951970686957/602280721125000)
(-9993820711238145239/105988466304900, 26356531702616563721862850759/1091158679801586843000)
(9412585030584093985617/43210222929593344, 973977570010304128722515174254759/8982138769007943977500672)
(-299639126247559938470543/12838863365175297024, 1726856939157955095415376600220154249/46003393111997125391777759232)
(176639922821001272486097/978459757869877504, 82724426635006026182580644466017689/967864259809924552238804992)
(-17385180187395206977463/150890329118416670784, 69889000801185611659009575746761078331/1853497944405953176302262338048)
(-1549721652556344507592241919/17408159370003856960900, 61470821064255616871162791187463951254771/2296832268225514186259318916773000)
(4058342045271982458765136177/12891166125518375349264, 264362105547253007829659977665954745576951/1463653607995471342911170548529088)

Commentary

The rational 3-isogenous partner of our accepted rank-10 Mordell curve obtained from the Burkhardt quartic with parameters (u,v,w) = (4,6,-4), specialized at t = -31/409.

last edited by jesper-petersen at 2026-10-23 21:41:37 UTC · history