curve #2853

y² = x³ − x² − 958595341735422253448874842847626704x + 361244367991028420756708447595507191492277326349839008

a-invariants: [0, -1, 0, -958595341735422253448874842847626704, 361244367991028420756708447595507191492277326349839008]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/8ℤ
conductor (N): 317396988702234542237136
discriminant (Δ): 453049812292754972368990024286652146861505188926279744886362970642279992907854559232
Faltings height: 18.6552
naive height: 260.1659
primes of bad reduction: 2, 3, 7, 11, 13, 17, 19, 37, 79, 109, 197, 479, 680249
regulator: 3778524.01294338643340287431970468299303754945398
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:25:22 UTC
last updated: 2026-09-26 20:25:22 UTC

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

(565237601212634066, 44042207341351033713822)
(2523381863043230225154/961, 118971517062884738300429680991230/29791)
(1051191516438152794722/1849, 336559033269697808566620450694/79507)
(465408004538003962962/841, 375768953991556794748494513098/24389)
(597965350847321449658258/923521, 97292468679453797994982752355479138/887503681)

Commentary

Dujella - Kazalicki - Peral (2021). Source: https://dujella.github.io/tors/z8old5.html (curve entry 59). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:25:22 UTC · history