curve #3329

y² + xy + y = x³ − 526819x + 147133002

a-invariants: [1, 0, 1, -526819, 147133002]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/6ℤ
conductor (N): 351130
discriminant (Δ): 138466710980
Faltings height: 1.7235
naive height: 51.1374
primes of bad reduction: 2, 5, 13, 37, 73
regulator: 23.1354015500200555098541939168503888796475
submitted by: David Renshaw
submitted at: 2026-09-26 20:58:42 UTC
last updated: 2026-09-26 20:58:42 UTC

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

(123, 9114)
(-542, 16809)

Commentary

Cremona 351130a1 = LMFDB 351130.a4: https://www.lmfdb.org/EllipticCurve/Q/351130/a/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 351130, minimal discriminant 138466710980, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:58:43 UTC · history