curve #1359

y² + xy + y = x³ − x² − 1844480924271965573x + 964182769053755713558006397

a-invariants: [1, -1, 1, -1844480924271965573, 964182769053755713558006397]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 46334137721085283821570
discriminant (Δ): -61131538514895307978217041549479527151206400
Faltings height: 8.7585
naive height: 137.7898
primes of bad reduction: 2, 3, 5, 7, 13, 31, 37, 71, 73, 103, 1723, 8237
regulator: 5513626.09463548366101463988402809433624879304480091372
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:38:20 UTC
last updated: 2026-09-24 17:38:20 UTC

(779260183, 234540928008)
(784138735, 1048550736)
(813238757983/1089, 64539112389845504/35937)
(7056889207/9, 2815544576/27)
(7057067707/9, 1989815476/27)
(24495729967/49, 4432951348620544/343)
(-809298113, 43896384276352)
(63512128303/81, 21273512192/729)

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:38:20 UTC · history