curve #1698

y² + y = x³ + x² − 10329067444876115930x + 12777744690738970527183509834

a-invariants: [0, 1, 1, -10329067444876115930, 12777744690738970527183509834]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/5ℤ
conductor (N): 50074305822776235
discriminant (Δ): -4684688953751182783480986510254889681317666013037696875
Faltings height: 9.5755
naive height: 142.9582
primes of bad reduction: 3, 5, 7, 11, 13, 41, 59, 89, 2539, 6101
regulator: 3976.1502808212202684426659089254002492316879111574
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:11:58 UTC
last updated: 2026-09-25 06:11:58 UTC

(1815099991, 3075886180867)
(28991735041/16, 211313871793993/64)
(5117542981, 306501045659077)
(2033027701, 13467660068362)
(4430554651, 232347181824712)
(37365335998, 7196883185743465)

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:11:58 UTC · history