curve #1695

y² + xy + y = x³ + x² − 288630794x + 1873567893062

a-invariants: [1, 1, 1, -288630794, 1873567893062]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 23832077997
discriminant (Δ): 22265821630729635625421937 ☆ record for ℤ/4ℤ torsion, rank ≥ 5
Faltings height: 3.6894 ☆ record for ℤ/4ℤ torsion, rank ≥ 5
naive height: 70.0556
primes of bad reduction: 3, 7, 13, 17, 29, 53, 257
regulator: 291.906224854004281038083987450317209001305199614
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:11:28 UTC
last updated: 2026-09-25 06:11:28 UTC

(13356, 626818)
(-4545, 1760548)
(-41385/4, 15538343/8)
(36407/4, 164699/8)
(-6909/4, 12314837/8)

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 06:11:28 UTC · history