curve #1149

y² = x³ + x² + 23x + 24

a-invariants: [0, 1, 0, 23, 24]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/3ℤ
conductor (N): 4396
discriminant (Δ): -861616
Faltings height: -0.1724 ☆ record for ℤ/3ℤ torsion, rank ≥ 2
naive height: 20.9763 ☆ record for ℤ/3ℤ torsion, rank ≥ 2
primes of bad reduction: 2, 7, 157
regulator: 1.77970962523723922563415883298609793992225
submitted by: David Renshaw
submitted at: 2026-09-23 21:37:38 UTC
last updated: 2026-09-23 21:37:38 UTC

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

(-1, 1)
(5, 17)

Commentary

Cremona 4396c1, rank exactly 2 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.00000-09999 . 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 21:37:38 UTC · history