curve #1081

y² + xy = x³ − 32075535x + 63675551097

a-invariants: [1, 0, 0, -32075535, 63675551097]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/12ℤ
conductor (N): 274170
discriminant (Δ): 360314065091912256000000
Faltings height: 3.2568
naive height: 63.4644
primes of bad reduction: 2, 3, 5, 13, 19, 37
regulator: 2.329118790521406941536427975914679315831
submitted by: David Renshaw
submitted at: 2026-09-23 15:26:09 UTC
last updated: 2026-09-23 15:26:09 UTC

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

(4494, 99213)

Commentary

Cremona 274170ck1 = LMFDB 274170.ck7: https://www.lmfdb.org/EllipticCurve/Q/274170/ck/7 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 274170, minimal discriminant 360314065091912256000000, torsion ℤ/12ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:26:09 UTC · history