curve #2854

y² + xy + y = x³ − 348661090280842928414956055328x − 69498818575042908305872415175040554816160994

a-invariants: [1, 0, 1, -348661090280842928414956055328, -69498818575042908305872415175040554816160994]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 384622999802924792910
discriminant (Δ): 626032099437861434339064631622743832757656892414551549746021937623716442935303289940250000
Faltings height: 15.9580
naive height: 215.6853
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 41, 53, 79, 227, 443, 2297
regulator: 19302.3520672418567224977331258055835051548693647
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:25:26 UTC
last updated: 2026-09-26 20:25:26 UTC

(-240171308953870, -621247444955021283753)
(-417386751107620, -1820451841460823094878)
(-266630790215083, -2123594247488660870277)
(-238064752167250, -113220964616005608573)
(15636454929856645/9, 1825056392925785937002669/27)

Voznyy (2021). Source: https://dujella.github.io/tors/z2z6old5.html (curve entry 18). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:25:26 UTC · history