curve #1492

y² + xy = x³ − 9133867357763769559583815213550x + 5898928970001153735077443080836755542607104132

a-invariants: [1, 0, 0, -9133867357763769559583815213550, 5898928970001153735077443080836755542607104132]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/12ℤ
conductor (N): 1639541630444190330
discriminant (Δ): 33736564439984489220424804930520511238248767591729688121158574830395925522581911998038016000000
Faltings height: 16.8364
naive height: 225.4822
primes of bad reduction: 2, 3, 5, 11, 13, 17, 37, 109, 127, 139, 337, 937
regulator: 5553.9410476890878622698296558417487964258241
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:36:19 UTC
last updated: 2026-09-25 00:36:19 UTC

(4204348247204497431676/1181569, 174459193311666615006931331416894/1284365503)
(-13576412615559927332163422276/16467437044081, 7580701806997379454577508422390093349013842/66825007731814094729)
(-5080488068040264016467071754116/1668493829534401, 5044765358471176212902746130566345127146382978/68153302822251414061601)

Torsion Z/12. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:36:19 UTC · history