curve #2014

y² + xy + y = x³ − 579495373032007322x − 10832607307280712098153820

a-invariants: [1, 0, 1, -579495373032007322, -10832607307280712098153820]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ
conductor (N): 13361790818375694829477764814281226
discriminant (Δ): 12403909894936917180891402217691300281075111544188485704
Faltings height: 9.2610
naive height: 134.3164
primes of bad reduction: 2, 13, 29, 41, 71, 73, 107, 149, 293, 857, 1193, 180241, 96875897
regulator: 5248980091602323.3343290579618821907153246555968111507110412868
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:00:15 UTC
last updated: 2026-09-26 05:00:15 UTC

(201732859001/64, -87910274652827407/512)
(2136105044, 92184797023004)
(438507784568347/125316, 8961413294703738126539/44361864)
(-2840378143026479305378/15597136361041, 580007511863386276509746854452656/61598098170522803161)
(298085645131864/225, -5146496839158848059268/3375)
(-579120220782619/7997584, 125419204173021386814803/22617167552)
(69575030246/49, 15450059089532768/343)
(1082140751789876/305809, 34759771775490645537527/169112377)
(225289824003394/12321, -3378600877951878961669/1367631)
(-3123846778879/6400, -6389282446688542471/512000)
(26487606774554/2401, -135996572947728432451/117649)
(5337243484951904/3441025, -339083409807082252845268/6383101375)

2-isogenous partner of curve#1209 (David Renshaw).

last edited by Steps Unbounded at 2026-09-26 21:39:11 UTC · history