curve #2834

y² + xy + y = x³ + x² − 44854x − 1361869

a-invariants: [1, 1, 1, -44854, -1361869]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 17958
discriminant (Δ): 4996042382905344
Faltings height: 1.7051
naive height: 43.7471
primes of bad reduction: 2, 3, 41, 73
regulator: 7.69237226097868054487336784384267725716504
submitted by: David Renshaw
submitted at: 2026-09-26 20:24:33 UTC
last updated: 2026-09-26 20:24:33 UTC

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

(261, 2059)
(-63, 1135)

Commentary

Cremona 17958j2 = LMFDB 17958.i4: https://www.lmfdb.org/EllipticCurve/Q/17958/i/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 17958, minimal discriminant 4996042382905344, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:24:33 UTC · history