curve #2969

y² + xy + y = x³ + x² − 62925x − 5683533

a-invariants: [1, 1, 1, -62925, -5683533]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 107070
discriminant (Δ): 2119690808010000
Faltings height: 1.6854
naive height: 44.7627
primes of bad reduction: 2, 3, 5, 43, 83
regulator: 12.4185157223613521437620514156128568939670
submitted by: David Renshaw
submitted at: 2026-09-26 20:30:55 UTC
last updated: 2026-09-26 20:30:55 UTC

Witness: 2 independent points log in to add more points →

(385, 5036)
(377, 4746)

Commentary

Cremona 107070r2 = LMFDB 107070.t4: https://www.lmfdb.org/EllipticCurve/Q/107070/t/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 107070, minimal discriminant 2119690808010000, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:30:55 UTC · history