curve #3312

y² + xy + y = x³ − x² + 97x − 313

a-invariants: [1, -1, 1, 97, -313]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/6ℤ
conductor (N): 1170
discriminant (Δ): -94910400
Faltings height: 0.2179
naive height: 25.3474
primes of bad reduction: 2, 3, 5, 13
regulator: 1.566843340808092581706402213315458758781
submitted by: David Renshaw
submitted at: 2026-09-26 20:55:58 UTC
last updated: 2026-09-26 20:55:58 UTC

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

(13, 48)

Commentary

Cremona 1170i1 = LMFDB 1170.h4: https://www.lmfdb.org/EllipticCurve/Q/1170/h/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1170, minimal discriminant -94910400, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:55:58 UTC · history