curve #2892

y² + xy = x³ − 1005616106232475912067151x + 149421536140955590484679512378606841

a-invariants: [1, 0, 0, -1005616106232475912067151, 149421536140955590484679512378606841]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 125026549077672232538730
discriminant (Δ): 55439183898058184156721431417927380376370738500793390795068159000976814080
Faltings height: 12.8433
naive height: 177.4165
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 23, 29, 73, 97, 547, 2399, 22877
regulator: 530333.2897303543511334272202976885987578935207250196
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:27:10 UTC
last updated: 2026-09-26 20:27:10 UTC

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

(62603623710, 294468440371266861)
(-171843292752, -563165401741104555)
(81838639761498/961, 7560165179333045088027/29791)
(6627954227184, -16871541381249849387)
(-554612937174690/2209, -64510325175796828854237/103823)
(6055399612704264/625, -468717877164630400753587/15625)
(-330616454896008/1369, -31150344990726063431145/50653)

Commentary

2-isogenous image of D-z6old678-126, rational kernel x=535079801286. 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 20:27:10 UTC · history