curve #1691

y² + y = x³ + x² − 4681323863817510x + 123661876023411492419210

a-invariants: [0, 1, 1, -4681323863817510, 123661876023411492419210]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/5ℤ
conductor (N): 24401110764753723
discriminant (Δ): -40480690392648311900201583484887626539538709963 ☆ record for ℤ/5ℤ torsion, rank ≥ 6
Faltings height: 7.8050 ☆ record for ℤ/5ℤ torsion, rank ≥ 6
naive height: 119.8668 ☆ record for ℤ/5ℤ torsion, rank ≥ 6
primes of bad reduction: 3, 7, 11, 13, 17, 19, 37, 2741, 248051
regulator: 2807.1539868551541337388361425926372275923672740868
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:10:48 UTC
last updated: 2026-09-25 06:10:48 UTC

(379452885/4, 5841936491387/8)
(139859208, 1484811570742)
(493176201/16, 5953070016589/64)
(4721991855/169, 266145899147608/2197)
(178446471, -2229482603849)
(-14774781, 435433304659)

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 06:10:48 UTC · history