curve #2692

y² + xy = x³ − 127315383961088129848470x + 17485155070163945330435232719141412

a-invariants: [1, 0, 0, -127315383961088129848470, 17485155070163945330435232719141412]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/9ℤ
conductor (N): 1023209767452210
discriminant (Δ): -29491232845915097376621080763420054932484854807738357463000000000
Faltings height: 11.7864
naive height: 171.2165
primes of bad reduction: 2, 3, 5, 13, 17, 107, 12619, 114299
regulator: 10845.191610897595571433216485265002878937767
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:17:59 UTC
last updated: 2026-09-26 20:17:59 UTC

(10291765410186/49, 1090296499085007474/343)
(-55979284852881/196, -479609533124397157833/2744)
(7648653205054401024924/24891688441, 337302481673686984286164322772798/3927186577025011)

van Beek (2015). Source: https://dujella.github.io/tors/z9old3.html (curve entry 12). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:17:59 UTC · history