curve #2796

y² + xy = x³ − 186734461375182851611482374885236743900x + 979124235576847382684597033191041431087287234552438410000

a-invariants: [1, 0, 0, -186734461375182851611482374885236743900, 979124235576847382684597033191041431087287234552438410000]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/10ℤ
conductor (N): 733110676848154824909690
discriminant (Δ): 2577079271418592157748476445692596737239745730527735368056419247523134515148282025200612976317036907295705436800000
Faltings height: 20.8150
naive height: 275.9819
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 41, 103, 157, 179, 1721, 5196749
regulator: 391794.8148281803252398215955119451296200526697
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:22:49 UTC
last updated: 2026-09-26 20:22:49 UTC

(-5710514747140022400, -43119071959774152308676399900)
(35512172342223738248711400/361201, 209680437320717911654215167303833570500/217081801)
(520496225635820845011448680/55965361, 2866472932142118340340507801774393572500/418676865641)
(17134135927565201341566386400/19997636569, 80967502846094281568437665397281398037119700/2827925780131997)

Dujella (2008). Source: https://dujella.github.io/tors/z10.html (curve entry 4). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:22:49 UTC · history