curve #1222

y² = x³ − 423412235407x + 107137669344845170

a-invariants: [0, 0, 0, -423412235407, 107137669344845170]
rank (lower bound): ≥ 14
torsion subgroup: trivial
conductor (N): 165397470686678259930364352553256
discriminant (Δ): -100561662177500382037661526352379648
Faltings height: 5.5283
naive height: 91.9489
primes of bad reduction: 2, 19, 12801337, 85002156768282885695519
regulator: 9314987488.69134842053742246222993894713178849888721374119503794051
submitted by: Michael Rubinstein
submitted at: 2026-09-24 14:26:57 UTC
last updated: 2026-09-24 14:26:57 UTC

(620589, -288756946)
(387161, 35241118)
(-241365, -441897440)
(196949, 177162326)
(401481, 43118638)
(270457, 111382142)
(184539, -187845704)
(337679, -51621784)
(2078497, -2864698058)
(-651542, -326227526)
(-324507, -458656474)
(444635, 82330040)
(3960022/9, -2095010452/27)
(366521, -34434878)

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

last edited by Michael Rubinstein at 2026-09-24 14:26:57 UTC · history