curve #1175

y² + xy + y = x³ − 2454x + 6872

a-invariants: [1, 0, 1, -2454, 6872]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/6ℤ
conductor (N): 14630 ☆ record for ℤ/6ℤ torsion, rank ≥ 2
discriminant (Δ): 923621042960
Faltings height: 0.9860 ☆ record for ℤ/6ℤ torsion, rank ≥ 2
naive height: 35.0294 ☆ record for ℤ/6ℤ torsion, rank ≥ 2
primes of bad reduction: 2, 5, 7, 11, 19
regulator: 4.85221169546016219826753015514312897087573
submitted by: David Renshaw
submitted at: 2026-09-23 21:38:22 UTC
last updated: 2026-09-23 21:38:22 UTC

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

(48, -8)
(49, 45)

Commentary

Cremona 14630g1, rank exactly 2 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.10000-19999 . 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 21:38:22 UTC · history