curve #1126

y² + xy + y = x³ + x² + 6x + 6

a-invariants: [1, 1, 1, 6, 6]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ
conductor (N): 2793
discriminant (Δ): -19551
Faltings height: -0.4889
naive height: 16.9784 ☆ record for ℤ/2ℤ torsion, rank ≥ 2
primes of bad reduction: 3, 7, 19
regulator: 1.74674723276811386769278198960130767805899
submitted by: David Renshaw
submitted at: 2026-09-23 21:36:49 UTC
last updated: 2026-09-23 21:36:49 UTC

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

(0, 2)
(3, 6)

Commentary

Cremona 2793a1, 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 21:36:50 UTC · history