curve #3213

y² + xy = x³ − x² − 8x + 11

a-invariants: [1, -1, 0, -8, 11]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ
conductor (N): 377
discriminant (Δ): 377
Faltings height: -0.6677
naive height: 17.9214
primes of bad reduction: 13, 29
regulator: 1.443894413560845861394701311935071148844
submitted by: David Renshaw
submitted at: 2026-09-26 20:42:58 UTC
last updated: 2026-09-26 20:42:58 UTC

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

(-2, 5)

Commentary

Cremona 377a1 = LMFDB 377.a3: https://www.lmfdb.org/EllipticCurve/Q/377/a/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 377, minimal discriminant 377, torsion ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:42:58 UTC · history