curve #2862

y² + xy = x³ − 209511385114746x + 1167133034644027591140

a-invariants: [1, 0, 0, -209511385114746, 1167133034644027591140]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 6110680457310
discriminant (Δ): 106208269421099600009675852422943283302400
Faltings height: 6.9042
naive height: 110.5410
primes of bad reduction: 2, 3, 5, 11, 13, 67, 73, 181, 1609
regulator: 328.790982145967766851911790978053816684498448048
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:25:48 UTC
last updated: 2026-09-26 20:25:48 UTC

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

(21155784, 78751027446)
(-6411756, 47404447350)
(452953722/49, -1547812945692/343)
(77243452/9, -29492552518/27)
(3076147140/361, -5235148040430/6859)

Commentary

2-isogenous to curve#1674 via the rational 2-torsion point x=-4210796. 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 20:25:49 UTC · history