curve #1354

y² = x³ − x² − 3139060840x + 67694106322816

a-invariants: [0, -1, 0, -3139060840, 67694106322816]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 92302917448300464
discriminant (Δ): 32518905602014564244554752 ☆ record for ℤ/2ℤ torsion, rank ≥ 8
Faltings height: 4.0575
naive height: 77.2152
primes of bad reduction: 2, 3, 17, 19, 59, 67, 83, 89, 179
regulator: 43063.7656149426510391383077495605912340515700686703984
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:37:29 UTC
last updated: 2026-09-24 17:37:29 UTC

(20100, 3566396)
(8286, 6500206)
(32004, 104252)
(38358, 1929262)
(-8732, 9717948)
(34416, -650704)
(37096, 1514736)
(32238, 24718)

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

last edited by Michael Rubinstein at 2026-09-24 17:37:29 UTC · history