curve #5710

y² + y = x³ − 140526740713547176

a-invariants: [0, 0, 1, 0, -140526740713547176]
c-invariants: [0, 121415103976504759848]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 1624653501828766194979144041489 ☆ record for Mordell curves, rank ≥ 11
discriminant (Δ): -8531034417607327515874950632986199643
Faltings height: 5.7653
naive height: 92.4915
primes of bad reduction: 3, 7, 60696141113723
regulator: 2203021102387644.85710198961220058757951494976722335706907462
submitted by: jesper-petersen
submitted at: 2026-10-24 14:42:47 UTC
last updated: 2026-10-24 14:42:47 UTC

(434511235842936/123765625, -9042638563950621111941/1376892578125)
(21631438918787748/8708435761, -3166852978371503092118207/812662516780759)
(57461928804530817/106170402244, -4642621820191246335958021/34594351526380472)
(2168293130940552/3958548889, 38434622376730514234296/249060020449213)
(14546062608176072148/1628382718561, 55472196715182625477950063832/2077948247884039441)
(6594939278138688666/847624042225, 16933682189991940706314217911/780377788835079625)
(1314322577309413833/2475323235856, 372919093846850955009150437/3894465652144018496)
(310220347469920594/15243606225, -172783313946807673502890297/1882051842569625)
(2331601250919806481/3080376010000, -2927115309339803523078604121/5406367935151000000)
(122057808763699658409/84818942478400, -1316312967700842625592057213077/781158710922170048000)
(71187082903036265641/135939043304100, 87943065708638355899628783689/1584952728205060089000)

The rationally 3-isogenous partner of the Burkhardt-quartic Mordell curve constructed with parameters (u,v,w)=(-1/5,0,6/5) at t=-340/57.

last edited by jesper-petersen at 2026-10-24 14:42:47 UTC · history