curve #1058

y² + xy = x³ − 454955x + 118072977

a-invariants: [1, 0, 0, -454955, 118072977]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/10ℤ
conductor (N): 6270 ☆ record for ℤ/10ℤ torsion, rank ≥ 1
discriminant (Δ): 301547812500000 ☆ record for ℤ/10ℤ torsion, rank ≥ 1
Faltings height: 1.8788
naive height: 50.6975
primes of bad reduction: 2, 3, 5, 11, 19
regulator: 2.707225460165105267594076124603183086339
submitted by: David Renshaw
submitted at: 2026-09-23 15:22:54 UTC
last updated: 2026-09-23 15:22:54 UTC

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

(418, 781)

Commentary

Cremona 6270r2 = LMFDB 6270.r2: https://www.lmfdb.org/EllipticCurve/Q/6270/r/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 6270, minimal discriminant 301547812500000, torsion ℤ/10ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:22:54 UTC · history