curve #812

y² + xy = x³ − x² − 438546442624x + 120392125493108044

a-invariants: [1, -1, 0, -438546442624, 120392125493108044]
rank (lower bound): ≥ 15
torsion subgroup: trivial
conductor (N): 431793384450914672704925243339122174
discriminant (Δ): -863586768901829345409850486678244348 ★ record for rank ≥ 15
Faltings height: 5.6380 ★ record for rank ≥ 15
naive height: 92.1822 ★ record for rank ≥ 15
primes of bad reduction: 2, 2797, 13469, 388477, 14752066382302142085667
regulator: 263818548239.76354305768355101205736891296057136096442359660547572376
submitted by: Michael Rubinstein
submitted at: 2026-09-21 00:39:24 UTC
last updated: 2026-09-21 00:39:24 UTC

(337505, -104214372)
(830308, 572896950)
(384631, -93015561)
(756838, -471550080)
(-349194, 480747530)
(633826, -311861496)
(997802, 821832750)
(225627, -181579850)
(458692, -125697522)
(690406, 382676864)
(-528813, -451866130)
(161302, -232137750)
(-226338, 456245570)
(-743271, 189393268)
(1954172, 2592469090)

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

last edited by Michael Rubinstein at 2026-09-21 00:39:24 UTC · history