curve #2725

y² + xy + y = x³ + x² − 53200x + 4740785

a-invariants: [1, 1, 1, -53200, 4740785]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 2370
discriminant (Δ): -163814400000000
Faltings height: 1.5471
naive height: 44.2759
primes of bad reduction: 2, 3, 5, 79
regulator: 1.742696834253500858545760119447842502969
submitted by: David Renshaw
submitted at: 2026-09-26 20:19:31 UTC
last updated: 2026-09-26 20:19:31 UTC

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

(93, 733)

Commentary

Cremona 2370i1 = LMFDB 2370.j6: https://www.lmfdb.org/EllipticCurve/Q/2370/j/6 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 2370, minimal discriminant -163814400000000, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:19:31 UTC · history