curve #2859

y² + xy = x³ − 3561865423528009610395543810x + 81454964632284157241813402084313871228100

a-invariants: [1, 0, 0, -3561865423528009610395543810, 81454964632284157241813402084313871228100]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/8ℤ
conductor (N): 468965404423650544410
discriminant (Δ): 25812930481056227322154830716230493339922335758593354520224586250215976985600000000
Faltings height: 14.6591
naive height: 201.9338
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 43, 67, 97, 449, 1409, 4649
regulator: 71311.1820333515500019384401531710125543107352671
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:25:41 UTC
last updated: 2026-09-26 20:25:41 UTC

(5949581008982, 245914531223693387432)
(-1195249703128, -292763685098693066518)
(71998581355220, 445232088662833121390)
(982331112925220, 30732830735127701753390)
(56005666625120, 240082528969829449490)

MacLeod (2012). Source: https://dujella.github.io/tors/z8old5.html (curve entry 4). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:25:41 UTC · history