curve #2880

y² = x³ − x² − 331999964186328512900x + 2327612294831641365690701258052

a-invariants: [0, -1, 0, -331999964186328512900, 2327612294831641365690701258052]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 395973919495628914440
discriminant (Δ): 1558268435409180652130660451933263919822501911140260201273600
Faltings height: 10.5155
naive height: 153.3686
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 53, 103, 167, 349, 32077
regulator: 61288.144676373455195074846664325341979223720963789
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:26:37 UTC
last updated: 2026-09-26 20:26:37 UTC

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

(11413318654, 158535977399800)
(2131189889, 1276611581208600)
(4902393233, 904344727306020)
(1363681784, 1370184634353990)
(10210152404, 47137942544550)
(10832642558, 48416892483960)

Commentary

Dujella (2006). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 100). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:26:37 UTC · history