curve #2717

y² + xy + y = x³ + x² − 60320x + 5539520

a-invariants: [1, 1, 1, -60320, 5539520]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 344955
discriminant (Δ): 669340980140625
Faltings height: 1.6244
naive height: 44.6359
primes of bad reduction: 3, 5, 13, 29, 61
regulator: 3.8337038863833645162171284002028344686012336
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:19:06 UTC
last updated: 2026-09-26 20:19:06 UTC

Witness: 3 independent points log in to add more points →

(188, -1037)
(3148, -177712)
(168, -512)

Commentary

2-isogenous to curve#1524 via the rational 2-torsion point x=-989/4. 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 20:19:06 UTC · history