curve #2770

y² + xy = x³ − 158098944776486419197823865299734138575x + 726993400178084973213410339257637465934549074905982884857

a-invariants: [1, 0, 0, -158098944776486419197823865299734138575, 726993400178084973213410339257637465934549074905982884857]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/10ℤ
conductor (N): 17569174278352986897510210
discriminant (Δ): 24590133588484883435830195931615233102387382301039546537447629224508071181981490779953216952248411807817259417600000
Faltings height: 20.8962
naive height: 275.4825
primes of bad reduction: 2, 3, 5, 7, 11, 17, 23, 61, 79, 149, 181, 709, 10711, 19709
regulator: 179087.4451211278996846883999466263160349637546
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:21:38 UTC
last updated: 2026-09-26 20:21:38 UTC

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

(1958323208465614043014/841, -470066390674717372678248369191503/24389)
(-999764275458691344759098/243049, 4333096796137033178932316224287842257/119823157)
(5315039329312426809387679/948676, -3819845937531111538650708226983657073/924010424)
(-51943843947723995507684/5329, -14250612788097319282264523302979009/389017)

Commentary

2-isogenous image of D-z10-003, rational kernel x=115502981116810136015/4. Source: https://dujella.github.io/tors/z10.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 20:21:38 UTC · history