curve #1219

y² + xy = x³ + x² − 413296473437x + 102731720232812529

a-invariants: [1, 1, 0, -413296473437, 102731720232812529]
rank (lower bound): ≥ 13
torsion subgroup: trivial
conductor (N): 87602268226431423767833962510
discriminant (Δ): -41063563231139729891172169926562500
Faltings height: 5.4870
naive height: 91.8649
primes of bad reduction: 2, 3, 5, 1949, 1498243000281023153203933
regulator: 470375855.9649436253755308533373089840048168755815608419043105938
submitted by: Michael Rubinstein
submitted at: 2026-09-24 14:26:15 UTC
last updated: 2026-09-24 14:26:15 UTC

(356708, 26155271)
(413458, 50100521)
(420818, -57925879)
(82633, 262911221)
(370178, -21743599)
(68008, 273715521)
(95458, 253229021)
(382208, -24701479)
(-604792, -362290729)
(366008, -22390729)
(16676192/49, -13312562047/343)
(304688, 71198921)
(519293, 167506121)

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

last edited by Michael Rubinstein at 2026-09-24 14:26:15 UTC · history