curve #1715

y² + xy + y = x³ + x² − 9041002229749526595x + 11136376154192276629287901345

a-invariants: [1, 1, 1, -9041002229749526595, 11136376154192276629287901345]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/5ℤ
conductor (N): 962007591612457390
discriminant (Δ): -6279577365752867720589937069003496671206245729690000000000
Faltings height: 9.8382
naive height: 142.6832
primes of bad reduction: 2, 5, 7, 11, 13, 19, 41, 43, 173, 269, 61651
regulator: 14477.967203026827892398340433666042159906087000504
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:14:48 UTC
last updated: 2026-09-25 06:14:48 UTC

(13115152043, 1465757069325838)
(1272040873, 41159123904088)
(5906536027/9, 1999740898017866/27)
(-1125522298997/361, 651344228922043642/6859)
(-22987344298973/8649, 102980980180386642566/804357)
(1629096267703/361, 1711128630088534642/6859)

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:14:48 UTC · history