curve #3032

y² + xy = x³ − 1706x + 26980

a-invariants: [1, 0, 0, -1706, 26980]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/6ℤ
conductor (N): 310
discriminant (Δ): 307520
Faltings height: 0.3799
naive height: 33.9394
primes of bad reduction: 2, 5, 31
regulator: 1.955238214193080114557686735051412748574
submitted by: David Renshaw
submitted at: 2026-09-26 20:34:09 UTC
last updated: 2026-09-26 20:34:09 UTC

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

(36, 94)

Commentary

Cremona 310b2 = LMFDB 310.a2: https://www.lmfdb.org/EllipticCurve/Q/310/a/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 310, minimal discriminant 307520, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:34:09 UTC · history