curve #1158

y² + xy + y = x³ + x² − 2436304x + 1462662170

a-invariants: [1, 1, 1, -2436304, 1462662170]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 35139
discriminant (Δ): 456807 ☆ record for ℤ/4ℤ torsion, rank ≥ 2
Faltings height: 1.8483
naive height: 55.7316
primes of bad reduction: 3, 13, 17, 53
regulator: 41.8735154166170449663005591167955204497154
submitted by: David Renshaw
submitted at: 2026-09-23 21:37:54 UTC
last updated: 2026-09-23 21:37:54 UTC

Witness: 2 independent points log in to add more points →

(957, 2476)
(8557, 774996)

Commentary

Cremona 35139c4, rank exactly 2 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.30000-39999 . Found by screening the local allgens tables for missing torsion size records; torsion and independence independently verified by the site.

last edited by David Renshaw at 2026-09-23 21:37:54 UTC · history