curve #1169

y² = x³ + x² − 7924x + 219776

a-invariants: [0, 1, 0, -7924, 219776]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 41496
discriminant (Δ): 10476149209344
Faltings height: 1.2158 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 2
naive height: 38.5467 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 2
primes of bad reduction: 2, 3, 7, 13, 19
regulator: 3.39723836545073581900781893152633885202454
submitted by: David Renshaw
submitted at: 2026-09-23 21:38:12 UTC
last updated: 2026-09-23 21:38:12 UTC

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

(74, 210)
(70, 114)

Commentary

Cremona 41496bb2, rank exactly 2 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.40000-49999 . 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 21:38:13 UTC · history