curve #227

y² + xy + y = x³ + x² − 3093247876694187640816x + 62533675385974785566766181200209

a-invariants: [1, 1, 1, -3093247876694187640816, 62533675385974785566766181200209]
rank (lower bound): ≥ 17
conductor (N): 79882435688106568827071480561070837976769102565133891830
naive height: 160.0641
Faltings height: 11.2834
discriminant (Δ): 204873677594335180956576449314454322564972911516245035826771353600
primes of bad reduction: 2, 3, 5, 13, 19, 10780355693401696197985355001494040212789352572892563
regulator: 4198210717650867.87015792172390323128899197641083758790537897585914004614
submitted by: Alexey Pozdnyakov
last updated: 2026-07-01 22:34:41

Witness: 17 independent points

(38378058149, -589021931997195)
(164608578773, 63352818096521829)
(41487998879, 2369029083476385)
(39304923569, 1294228037093685)
(23928280001, -1489311095968587)
(48788824931, 5268011129112945)
(51542641763, -6326948724258261)
(294670874773, -157282021941860603)
(55080221653, 7698087202523749)
(38320924949, -521149441872795)
(-20697282539, -10848457303964795)
(42781590599, -2915709540138345)
(45550376581, -4018065536875755)
(158788250041/9, -99024503808654185/27)
(-14288127963, -10188882244057499)
(25640408453, 279851614094949)
(25664045453, -227764996973403)

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_u2_v5 with specialization T=2307/1.

last edited by Alexey Pozdnyakov at 2026-06-25 23:18:44 · history