curve #1068

y² + xy = x³ − 749461x + 263897441

a-invariants: [1, 0, 0, -749461, 263897441]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/12ℤ
conductor (N): 30030
discriminant (Δ): -3157693080314572800
Faltings height: 2.3012
naive height: 52.3058
primes of bad reduction: 2, 3, 5, 7, 11, 13
regulator: 1.635056160791804448774403022446666923237
submitted by: David Renshaw
submitted at: 2026-09-23 15:24:00 UTC
last updated: 2026-09-23 15:24:00 UTC

Witness: 1 independent point log in to add more points →

(394, 5263)

Commentary

Cremona 30030bt1 = LMFDB 30030.bt7: https://www.lmfdb.org/EllipticCurve/Q/30030/bt/7 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 30030, minimal discriminant -3157693080314572800, torsion ℤ/12ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:24:00 UTC · history