curve #231

y² + xy = x³ − 2356513159556540884992x + 45035945457332407869731977363456

a-invariants: [1, 0, 0, -2356513159556540884992, 45035945457332407869731977363456]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 90822486465985344845462123297288403822069848710579842463634
naive height: 159.2932
Faltings height: 11.1753
discriminant (Δ): -38688926074726301138649337130672103413740602433127643612028665856
primes of bad reduction: 2, 13, 863, 31787682271043383, 915104046386062103, 139148940743185753507
regulator: 28452934182224966.6012110193994401286027763716771254315599232725266211317
submitted by: Alexey Pozdnyakov
submitted at: 2026-06-25 23:18:48 UTC
last updated: 2026-07-01 22:34:41 UTC

Witness: 17 independent points

(5248336256, -5728242982433280)
(27508940752, 1013855318237440)
(23878844464, -1543006612856576)
(19737266304, -2492731442864768)
(18373533504, -2818010805775168)
(92182935072, 24721361145021440)
(32273096144, -1611878798589648)
(30975335294, -1327459810236596)
(21214458350, -2142773068047284)
(64610326912, -12747436122575360)
(26832062936, 1060098553036264)
(-37518610240, -8979742835342336)
(-53256582608, 4414330307269840)
(-46520921028, -7347269609014412)
(1465391525200/49, 392432565204690688/343)
(531387441448/9, 285394583350887880/27)
(255616230159/4, 99731229782086477/8)

Commentary

Generated with assistance from OpenAI Codex, based on GPT-5. Method: Generalized Mestre/Fermigier quartic-family search: Mestre-Nagao stage sieve, high-M rescore, exact-height triage, and conductor analysis. Candidate came from family mestre_um2_vm4 with specialization T=79/2.

last edited by Alexey Pozdnyakov at 2026-06-25 23:18:48 UTC · history