curve #2978

y² + xy + y = x³ − x² − 19x − 14

a-invariants: [1, -1, 1, -19, -14]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 791
discriminant (Δ): 271313
Faltings height: -0.2578
naive height: 20.3972
primes of bad reduction: 7, 113
regulator: 2.789864343391251692042012119574341836409
submitted by: David Renshaw
submitted at: 2026-09-26 20:31:34 UTC
last updated: 2026-09-26 20:31:34 UTC

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

(68, 522)

Commentary

Cremona 791c1 = LMFDB 791.a4: https://www.lmfdb.org/EllipticCurve/Q/791/a/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 791, minimal discriminant 271313, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:31:34 UTC · history