curve #1621

y² + xy = x³ − x² − 3288225561486891858286430940x + 72555342130711253732719919997624790986000

a-invariants: [1, -1, 0, -3288225561486891858286430940, 72555342130711253732719919997624790986000]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 5947350746830783290
discriminant (Δ): 1268844011324778633871750984171060847802453604854886181080680882752923107038990400
Faltings height: 14.5366
naive height: 201.6940
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 31, 41, 67, 97, 109, 227
regulator: 2966.381820721331656257413156152455451609583227
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:44:15 UTC
last updated: 2026-09-25 01:44:15 UTC

(33624505835152, 2548987483370127684)
(143911788900560369280/5555449, 903251296040227937853366351060/13094193293)
(368153140522448565/11449, 10157331995479690746309945/1225043)
(5993099699979714845440/129208689, 206799440667021144947594927351620/1468715167863)

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 01:44:15 UTC · history