curve #3305

y² + xy + y = x³ − x² − 421312x + 105362906

a-invariants: [1, -1, 1, -421312, 105362906]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 301835
discriminant (Δ): 20222945
Faltings height: 1.5287
naive height: 50.4670
primes of bad reduction: 5, 17, 53, 67
regulator: 75.0449208322522443392470236208540186280691
submitted by: David Renshaw
submitted at: 2026-09-26 20:54:50 UTC
last updated: 2026-09-26 20:54:50 UTC

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

(-2725/4, 72401/8)
(226504/225, 87635903/3375)

Commentary

Cremona 301835b1 = LMFDB 301835.b3: https://www.lmfdb.org/EllipticCurve/Q/301835/b/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 301835, minimal discriminant 20222945, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:54:50 UTC · history