curve #3339

y² = x³ + x² − 373849x + 86412071

a-invariants: [0, 1, 0, -373849, 86412071]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 9353416128
discriminant (Δ): 108952781389369344
Faltings height: 2.0629
naive height: 50.1084
primes of bad reduction: 2, 3, 7, 107, 193, 337
regulator: 18700.5920631713217489919745345876718366223858459
submitted by: David Renshaw
submitted at: 2026-09-26 21:03:01 UTC
last updated: 2026-09-26 21:03:01 UTC

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

(39468161/6400, 246797926209/512000)
(4805/4, 296343/8)
(526817/784, -258868665/21952)
(46625/16, 9863271/64)
(26223425045/63266116, -847735164414369/503218686664)

Commentary

Rationally isogenous to curve#806 (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 21:03:01 UTC · history