curve #2878

y² + xy = x³ − x² − 25x − 39

a-invariants: [1, -1, 0, -25, -39]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 370
discriminant (Δ): 136900
Faltings height: -0.2701
naive height: 21.2926
primes of bad reduction: 2, 5, 37
regulator: 1.209982416984587453877766694425763746358
submitted by: David Renshaw
submitted at: 2026-09-26 20:26:32 UTC
last updated: 2026-09-26 20:26:32 UTC

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

(8, 11)

Commentary

Cremona 370a2 = LMFDB 370.b2: https://www.lmfdb.org/EllipticCurve/Q/370/b/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 370, minimal discriminant 136900, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:26:32 UTC · history