curve #2772

y² = x³ − x² − 2854146384555022744x − 314500829899221174494262656

a-invariants: [0, -1, 0, -2854146384555022744, -314500829899221174494262656]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 198425172913968
discriminant (Δ): 1445290328176598582372191974828917288861611699013105501184
Faltings height: 9.6581
naive height: 139.0995
primes of bad reduction: 2, 3, 7, 11, 13, 43, 53, 73, 103, 241
regulator: 3417.660717931345791056081138496159216584618200
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:21:45 UTC
last updated: 2026-09-26 20:21:45 UTC

Witness: 4 independent points log in to add more points →

(1779892412, 15625462894860)
(-600024131591/1600, -1697033795746381677/64000)
(182911948440, -78224820918092128)
(41430136437308229/2553604, -8386697639202420897265445/4080659192)

Commentary

2-isogenous to curve#1635 via the rational 2-torsion point x=3262736849. 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 20:21:45 UTC · history