curve #3309

y² + y = x³ − x² − 91630x + 10706542

a-invariants: [0, -1, 1, -91630, 10706542]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/5ℤ
conductor (N): 99803
discriminant (Δ): -341206596203
Faltings height: 1.4243
naive height: 45.8902
primes of bad reduction: 11, 43, 211
regulator: 16.0007389538465638893817673556506958246190
submitted by: David Renshaw
submitted at: 2026-09-26 20:55:29 UTC
last updated: 2026-09-26 20:55:29 UTC

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

(175, 6)
(601, 13128)

Commentary

Cremona 99803b1 = LMFDB 99803.a1: https://www.lmfdb.org/EllipticCurve/Q/99803/a/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 99803, minimal discriminant -341206596203, torsion ℤ/5ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:55:29 UTC · history