curve #3097

y² + xy = x³ − 1281493142199716912383484016491195x + 20908478821228455374087389955630487236070347099025

a-invariants: [1, 0, 0, -1281493142199716912383484016491195, 20908478821228455374087389955630487236070347099025]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/4ℤ
conductor (N): 20468006001635161782527819002994903297490
discriminant (Δ): -54167080167818807754176477241179343461774692239631086248934251271662500937436627214749237374400000000
Faltings height: 18.0484
naive height: 240.6516
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 59, 151, 173, 271, 4273, 697441, 1256873
regulator: 381016438.9966447516442316032117166255375228624047348972097
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:37:10 UTC
last updated: 2026-09-26 20:37:10 UTC

Witness: 10 independent points log in to add more points →

(-1884428609245490, -4828733727563649610956095)
(9999761497788040, 3015589736530490299309855)
(12200758408015870, 2662607223124380557977105)
(4933348790184430, 3834904647907043298422065)
(14461367628578290, 2323931548228764087838105)
(-2033604490069460, -4848310938042222755152895)
(8994062137272190, 3179655310614273671989105)
(16053683488503262, 2114984845243170564101137)
(26966762358435790, 2441547962033335259143105)
(-31857718537505168, -5422275775738654103544119)

Commentary

Eroshkin (2008). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 24). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:37:10 UTC · history