curve #2797

y² + xy = x³ − 23403453875708065582617252610904740290x + 56740472134219104191564989530383862470828076555856412100

a-invariants: [1, 0, 0, -23403453875708065582617252610904740290, 56740472134219104191564989530383862470828076555856412100]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/9ℤ
conductor (N): 25399371345088353798573570
discriminant (Δ): -570426848100604268054783416422819302083521748807688110617055268069765526954261647878701913930305423413391000000000
Faltings height: 20.5364
naive height: 270.2793
primes of bad reduction: 2, 3, 5, 7, 13, 19, 23, 73, 149, 181, 557, 1051, 18472823
regulator: 2475716.173923679946255159015774688126898350682
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:22:53 UTC
last updated: 2026-09-26 20:22:53 UTC

Witness: 4 independent points log in to add more points →

(1183994360874580962, 5539917734246665612825389372)
(-2124831061815491209344/625, -153897336826049953226494844248254/15625)
(-25383574246817605139361514218789870/11541875487800641, -12248431721078582644888104112139415756148879568434740/1239979705847820288430561)
(11039168903707688516615907465345318179937903715079971086630/254035585383892857719517730338266639041, 1153050961572815973856652265360603781222807961488616072729885712260634333824958537635010/4048944608766863824144593988025419443424110442121986160161)

Commentary

Dujella - Petricevic - Rathbun (2022). Source: https://dujella.github.io/tors/z9.html (curve entry 6). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:22:53 UTC · history