curve #2818

y² + xy + y = x³ + x² − 6074963938x − 109686071683594

a-invariants: [1, 1, 1, -6074963938, -109686071683594]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 47961031575
discriminant (Δ): 9151484523071323132144297265625
Faltings height: 4.6411
naive height: 79.1959
primes of bad reduction: 3, 5, 29, 181, 4201
regulator: 2417.82385641394809644115777002467079828703694930
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:23:48 UTC
last updated: 2026-09-26 20:23:48 UTC

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

(1667909/16, 1260331407/64)
(-49661725/1156, -332687539827/39304)
(-20521, 2527632)
(4963100/49, -6096697209/343)
(7882811, -22134910230)

Commentary

2-isogenous to curve#1707 via the rational 2-torsion point x=33265. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:23:48 UTC · history