curve #3344

y² = x³ − x² − 3903836x + 2970119790

a-invariants: [0, -1, 0, -3903836, 2970119790]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 21524842560
discriminant (Δ): 32736594928440000
Faltings height: 2.3679
naive height: 57.1460
primes of bad reduction: 2, 3, 5, 13, 23, 31, 41, 59
regulator: 2902.72585066126569603990445913001542027321304397
submitted by: David Renshaw
submitted at: 2026-09-26 21:05:48 UTC
last updated: 2026-09-26 21:05:48 UTC

Witness: 5 independent points log in to add more points →

(897597/4, -850362975/8)
(123597/4, -43364775/8)
(463051/49, -308681626/343)
(20197/4, -2676875/8)
(877833/256, -708164325/4096)

Commentary

Rationally isogenous to curve#1912 (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 5 carries over. Torsion ℤ/2ℤ.

last edited by David Renshaw at 2026-09-26 21:05:48 UTC · history