curve #3338

y² = x³ − x² − 192387489x + 462048064929

a-invariants: [0, -1, 0, -192387489, 462048064929]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 144443213376
discriminant (Δ): 363531581098062408489959424
Faltings height: 3.7912
naive height: 68.8387
primes of bad reduction: 2, 3, 7, 11, 23, 31, 71, 193
regulator: 8067.58113245862448473842897933880071228812990674
submitted by: David Renshaw
submitted at: 2026-09-26 21:02:52 UTC
last updated: 2026-09-26 21:02:52 UTC

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

(-1487, 863040)
(67677/4, -11454345/8)
(5937/16, 40004415/64)
(-723/4, 5638815/8)
(679137/49, 232087680/343)

Commentary

Rationally isogenous to curve#1644 (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 × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-26 21:02:52 UTC · history