curve #2891

y² + xy + y = x³ − x² − 1317314312228800268674787402x + 18402728930762603712606815033717512395401

a-invariants: [1, -1, 1, -1317314312228800268674787402, 18402728930762603712606815033717512395401]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 1855529015792879526484770
discriminant (Δ): 11349211283493786614190300840325130622696634758278789388360900169728000
Faltings height: 13.8461
naive height: 198.9498
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 23, 83, 719, 56807, 10631519
regulator: 23351073.44604075189124340461726080616479603215737313
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:27:07 UTC
last updated: 2026-09-26 20:27:07 UTC

Witness: 7 independent points log in to add more points →

(545581506150889/25, -866620726782491457573/125)
(20962160120209, -58156797066976521)
(30296616017521, 79381158175387391319)
(20955105124261, -2216217608086241)
(1273651704680379241/57121, -146870456720892645954591039/13651919)
(203931098788240739578489/9743071849, 182528813095967528625642261656797/961709392999243)
(1707019240611361/81, -691289034488538009569/729)

Commentary

2-isogenous image of D-z6old678-135, rational kernel x=-10477415138799. Source: https://dujella.github.io/tors/z6old678.html. Independent witness points transported by 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 20:27:07 UTC · history