curve #1622

y² + xy = x³ − 21800665795002485450059585x − 36208335237581709427665275459789550775

a-invariants: [1, 0, 0, -21800665795002485450059585, -36208335237581709427665275459789550775]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 687236202706563510
discriminant (Δ): 96744791467033609771346051774455084012857520301266704254538804507805929000000
Faltings height: 13.5138
naive height: 186.6456
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 41, 103, 131, 241, 439
regulator: 14047.60312173900275850735156789971228645433427
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:45:16 UTC
last updated: 2026-09-25 01:45:16 UTC

(-173819219151178120/54289, 11101597584474990987629755/12649337)
(6741054520070, 11097651674497137815)
(4941619742861450676950/76020961, 346459070671104924124290555740585/662826758959)
(12624595451776025434262/1617567961, 1067113803235446748145515725562313/65056965823459)

Torsion Z/6+Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:45:16 UTC · history