curve #1223

y² + xy = x³ − x² − 111652073395x + 14513129257645321

a-invariants: [1, -1, 0, -111652073395, 14513129257645321]
rank (lower bound): ≥ 14
torsion subgroup: trivial
conductor (N): 191217850521411534913210243850810
discriminant (Δ): -1912178505214115349132102438508100
Faltings height: 5.1966
naive height: 87.9508
primes of bad reduction: 2, 5, 19121785052141153491321024385081
regulator: 12686311134.4129539202070675685674075829882232004748997015421824297
submitted by: Michael Rubinstein
submitted at: 2026-09-24 14:27:07 UTC
last updated: 2026-09-24 14:27:07 UTC

(212688, 19571891)
(176798, -17394809)
(165628, -23831739)
(-56792, 143802171)
(127505, -48538851)
(537563, -331681829)
(175073, 18131341)
(-301762, 144119191)
(1828039/9, 392736494/27)
(233208, -34148579)
(1483348, 1763552741)
(111753, 58521586)
(114846, -56671013)
(173713, 18878621)

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

last edited by Michael Rubinstein at 2026-09-24 14:27:07 UTC · history