curve #3094

y² + xy = x³ − 1034642810304700336989303292996335x + 27194354320720666208457979454230524027566043738297

a-invariants: [1, 0, 0, -1034642810304700336989303292996335, 27194354320720666208457979454230524027566043738297]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/4ℤ
conductor (N): 43591641500121819666966659383620704342130
discriminant (Δ): -248593711501176012387288605140202038290848457422247375981053992534809736220238107716170369662400000000
Faltings height: 18.1453
naive height: 241.1773
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 61, 83, 101, 107, 137, 439, 37463414931029
regulator: 151098817.6598393166631180526409645000873447168077129966733
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:37:02 UTC
last updated: 2026-09-26 20:37:02 UTC

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

(1963070251109334, 5017055188546855513152333)
(2685645541820454, 4943181282395407331179293)
(7997842751105574, 4408064167520510706622653)
(9767429295482214, 4245043305621547405927773)
(-5651061635916666, -5732427126985005778937667)
(16574454263852334, 3820853916529487973711333)
(7436414620847334, 4462236776055147090486333)
(19476238825878894, 3798842748743389505855013)
(-6605865818580816, -5808683381863099996969317)
(13748357584511334, 3945680279355505842090333)

Commentary

Eroshkin (2010). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 33). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:37:03 UTC · history