curve #225

y² + xy = x³ − 74930448115659308831654455245038x + 249563452537886885000166950293580142396024130692

a-invariants: [1, 0, 0, -74930448115659308831654455245038, 249563452537886885000166950293580142396024130692]
rank (lower bound): ≥ 19
conductor (N): 305612822977927350087196447812113421419402448463094784488568526950
naive height: 231.7959
Faltings height: 17.0534
discriminant (Δ): 19165526853195419552478026879498587507276138078291075987245289519588640497575159258293376000000
primes of bad reduction: 2, 3, 5, 11, 13, 17, 37, 79, 89, 6379, 28166397753511, 17930509179380017127220936003343570961
regulator: 315606972157921062.9287695173038203469728749809356091846689042492693943318539
submitted by: Alexey Pozdnyakov
last updated: 2026-07-01 22:31:40

Witness: 19 independent points

(4882261436067532, 10455925384379314803634)
(5710070459686252, -88778475080120654768126)
(5439993856112332, 54137910929405459176834)
(4838847837782332, 16892856695505555928834)
(4909045600971652, -5312630013962056985126)
(3784167745652668, -142137498393290391417470)
(4343791276627132, -77731268535751116304766)
(9639568465898602, -650374750837561993346576)
(5081960163093772, 4269076187506464793714)
(1760155168566532, -350895220399651061347166)
(7231883051682652, -293093259063868129124126)
(4907638739041852, 5653244447855662364674)
(20904343537780483/4, 212447116156674922899167/8)
(9283304033644872, -594973946534384517013386)
(328199221517367772, 187956238503253577989464514)
(4615861527249346, -45180147467781491555720)
(5156388008664772, -17110583905139451344486)
(5460212511620152, 56724109510237623938374)
(-187591819551050534312/18769, 17143338594991268980322143922/2571353)

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, conductor analysis, and GP famcert certification. Candidate came from family mestre_u3_vm1 with specialization T=15619/18.

last edited by Alexey Pozdnyakov at 2026-06-25 23:18:42 · history