curve #1179

y² + xy = x³ − 1927252846x + 32565217284740

a-invariants: [1, 0, 0, -1927252846, 32565217284740]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 356730 ☆ record for ℤ/2ℤ × ℤ/6ℤ torsion, rank ≥ 2
discriminant (Δ): 73844065002898967040000 ☆ record for ℤ/2ℤ × ℤ/6ℤ torsion, rank ≥ 2
Faltings height: 3.8239 ☆ record for ℤ/2ℤ × ℤ/6ℤ torsion, rank ≥ 2
naive height: 75.7517
primes of bad reduction: 2, 3, 5, 11, 23, 47
regulator: 11.4861635326739247176034663700851410765169
submitted by: David Renshaw
submitted at: 2026-09-23 21:38:32 UTC
last updated: 2026-09-23 21:38:32 UTC

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

(25358, -9754)
(26108, 198146)

Commentary

Cremona 356730by2, rank exactly 2 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.350000-359999 . 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 21:38:32 UTC · history