curve #1153

y² = x³ + x² − 2873x + 58312

a-invariants: [0, 1, 0, -2873, 58312]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/3ℤ
conductor (N): 310868
discriminant (Δ): 657796688
Faltings height: 0.6790
naive height: 35.5033
primes of bad reduction: 2, 23, 31, 109
regulator: 8.3989161246526378713516746615191052021985075
submitted by: David Renshaw
submitted at: 2026-09-23 21:37:46 UTC
last updated: 2026-09-23 21:37:46 UTC

Witness: 3 independent points log in to add more points →

(31, 1)
(29, 15)
(43, 127)

Commentary

Cremona 310868a1, rank exactly 3 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.310000-319999 . 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 21:37:46 UTC · history