curve #811

y² + xy = x³ + x² − 1661237516922x + 1018021144936251600

a-invariants: [1, 1, 0, -1661237516922, 1018021144936251600]
rank (lower bound): ≥ 15
torsion subgroup: trivial
conductor (N): 265121998882424427980422961463765954 ★ record for rank ≥ 15
discriminant (Δ): -154301003349571017084606163571911785228
Faltings height: 6.0415
naive height: 96.4519
primes of bad reduction: 2, 3, 97, 16067, 28352279862699561990995070841
regulator: 130760975253.96212528426593288161049425753611703318311527202101340871
submitted by: Michael Rubinstein
submitted at: 2026-09-21 00:35:00 UTC
last updated: 2026-09-21 00:35:00 UTC

(1077288, -692374848)
(2543346, -3640617486)
(1839126, -2046263406)
(2736491/4, -3595771303/8)
(-574525, -1334930105)
(982014, -578133216)
(307302, 732334962)
(134642, -892698084)
(-673077, 1353568455)
(-1406307, 757658295)
(-545619, -1327128201)
(1925183/4, 4593480663/8)
(-150150, 1124384130)
(2141475, 2697290055)
(-131429, 1110959815)

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

last edited by Michael Rubinstein at 2026-09-21 00:35:00 UTC · history