curve #3291

y² + xy + y = x³ + x² − 415x − 1108

a-invariants: [1, 1, 1, -415, -1108]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 46965
discriminant (Δ): 4197402945
Faltings height: 0.5379
naive height: 29.6986
primes of bad reduction: 3, 5, 31, 101
regulator: 9.80735191701645501408687024646217732410698
submitted by: David Renshaw
submitted at: 2026-09-26 20:52:34 UTC
last updated: 2026-09-26 20:52:34 UTC

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

(-4, 24)
(46, 259)

Commentary

Cremona 46965b1 = LMFDB 46965.a4: https://www.lmfdb.org/EllipticCurve/Q/46965/a/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 46965, minimal discriminant 4197402945, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:52:34 UTC · history