curve #2873

y² = x³ − x² − 1621105850715834564900x + 4979606331160862237085144928452

a-invariants: [0, -1, 0, -1621105850715834564900, 4979606331160862237085144928452]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 174140970298157782920
discriminant (Δ): 261943314808113584828175457033067436235611494555073979459539360000
Faltings height: 11.2430
naive height: 158.1258
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 29, 31, 37, 41, 47, 67, 109, 163
regulator: 8988.4027918010209961788638229313779100335210767938
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:26:18 UTC
last updated: 2026-09-26 20:26:18 UTC

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

(1291128254, 1699618513398080)
(-9589966542, 4432154369225880)
(-166732650939/4, 2867877947917125/8)
(-987086238936/25, 340817455790473662/125)
(6033839983202, 14821119830299337984)
(-14560799125208/3721, 761767378800794319954/226981)

Commentary

Ansaldi - Ford - George - Mugo - Phifer (2005). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 72). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:26:18 UTC · history