curve #1697

y² + xy + y = x³ − x² − 1884732791x + 465954679391262

a-invariants: [1, -1, 1, -1884732791, 465954679391262]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/4ℤ
conductor (N): 33400306665873
discriminant (Δ): -93364477236902748911574149376543 ☆ record for ℤ/4ℤ torsion, rank ≥ 6
Faltings height: 4.8140 ☆ record for ℤ/4ℤ torsion, rank ≥ 6
naive height: 81.0734 ☆ record for ℤ/4ℤ torsion, rank ≥ 6
primes of bad reduction: 3, 7, 43, 109, 157, 193, 3733
regulator: 5439.9037070703575668917758570454759402542429085381
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:11:48 UTC
last updated: 2026-09-25 06:11:48 UTC

(210185, 96617583)
(-19173805/484, 233119110339/10648)
(30884, 20893974)
(-79282, -10778751)
(843584, 773657349)
(-2481220/289, 107827938558/4913)

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:11:48 UTC · history