curve #3347

y² = x³ − x² − 2004811745x + 27169577284641

a-invariants: [0, -1, 0, -2004811745, 27169577284641]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 91109902081901376
discriminant (Δ): 196823683706795970083091873792
Faltings height: 4.3344
naive height: 75.8701
primes of bad reduction: 2, 3, 17, 89, 223, 257, 3617
regulator: 11381785.6965470785016352283955406762578272205266959358
submitted by: David Renshaw
submitted at: 2026-09-26 21:06:49 UTC
last updated: 2026-09-26 21:06:49 UTC

Witness: 8 independent points log in to add more points →

(-2909, 5742556)
(-43377, -5702088)
(-29697, -7779168)
(-5912, 6230197)
(41983, -4122848)
(-15089, -7347416)
(36003, 1287132)
(35416, -766781)

Commentary

Rationally isogenous to curve#1353 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 8 carries over. Torsion ℤ/2ℤ.

last edited by David Renshaw at 2026-09-26 21:06:49 UTC · history