curve #2874

y² + xy = x³ − 1412825737585924163044x + 15284155642547476371073178165264

a-invariants: [1, 0, 0, -1412825737585924163044, 15284155642547476371073178165264]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 3909968370958694691318
discriminant (Δ): 79569395352540341075395882036325863181216044329352639168799879424
Faltings height: 11.1628
naive height: 157.7132
primes of bad reduction: 2, 3, 7, 17, 29, 43, 47, 71, 431, 11351, 268993
regulator: 225868.91960327324621549521101455562582648897806950
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:26:22 UTC
last updated: 2026-09-26 20:26:22 UTC

Witness: 6 independent points log in to add more points →

(-4710088480, -4672705304733532)
(10971680384, 1050627482515964)
(5142674960, 2855599110883388)
(190936944656, 81893102282965052)
(188694106912, 80419019486556004)
(47485021091/4, 3441975241405087/8)

Commentary

Dujella (2005). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 73). Published independent points; exact point coordinates checked.

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