curve #2876

y² = x³ − x² − 4664630695650596406400x + 122611657721145018740841654400000

a-invariants: [0, -1, 0, -4664630695650596406400, 122611657721145018740841654400000]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 51197573456019679920
discriminant (Δ): 1263697382202885363203778072422808403136020331210660544552960000
Faltings height: 11.1362
naive height: 161.2965
primes of bad reduction: 2, 3, 5, 7, 11, 19, 29, 79, 181, 479, 719, 1021
regulator: 92398.202506826902495188280920264857393310786875130
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:26:25 UTC
last updated: 2026-09-26 20:26:25 UTC

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

(28260480960, 3654766624544480)
(-12857421920, 13433587750450560)
(13143969210, 7973123554358270)
(34512505410, 1652834075535170)
(91860783045, 21662718643569190)
(38608886722, 260090980468158)

Commentary

Dujella (2006). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 98). Published independent points; exact point coordinates checked.

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