curve #2839

y² + xy = x³ − 12151449801116771364158721464095x + 16303853171210911871908176340222708651618600025

a-invariants: [1, 0, 0, -12151449801116771364158721464095, 16303853171210911871908176340222708651618600025]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/7ℤ
conductor (N): 18508351164730219223970
discriminant (Δ): 1975840297828412229004318741356701020847837779563155990558007000009981925572656250000000
Faltings height: 16.3266
naive height: 226.3386
primes of bad reduction: 2, 3, 5, 7, 11, 17, 23, 107, 109, 113, 15548563603
regulator: 115617.969666636233433173746987187745284314625023
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:24:45 UTC
last updated: 2026-09-26 20:24:45 UTC

(2012780061897290, 9918904791182773505)
(295193067596090, 112882913713614812821205)
(2797902037885640, 64868942660403853981205)
(2005584289115840, 543238680070107868955)
(521254825746693017/256, 7516252265355007774821851/4096)

Eroshkin (2009). Source: https://dujella.github.io/tors/z7old5.html (curve entry 12). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:24:45 UTC · history