curve #230

y² + xy = x³ − x² − 681626561473549068876x + 6906843129225400827472871428396

a-invariants: [1, -1, 0, -681626561473549068876, 6906843129225400827472871428396]
rank (lower bound): ≥ 17
conductor (N): 5780619339498795734844787336993702205165528840080081279506
naive height: 155.5433
Faltings height: 10.8189
discriminant (Δ): -339935100878566181983282564139251651876964088969749259722629836
primes of bad reduction: 2, 3, 11, 191453, 42921536569, 7087432437710059, 501282810266440502658469
regulator: 84981055456264679.3117933149443931503433513638479714063571863841096814388
submitted by: Alexey Pozdnyakov
last updated: 2026-07-01 22:34:40

Witness: 17 independent points

(16043886086, 317326611497870)
(17280696650, 536895191338436)
(14167766489, -305867682555505)
(16535679509, 396241732694276)
(16013767470, 313067686622764)
(18926463036, -886423879429906)
(-11684436811, -3643623591778009)
(10290536150, 991084187061164)
(13790371721, -359915883876241)
(12747069311, -537914403677005)
(39502758506, -6451647565937326)
(-10653514054, 3599924151318020)
(13815574626, -356041517678630)
(-31989738925/4, -27535079488466087/8)
(-30174525310, 25235897491514)
(2983714754780/121, 3003650211440656834/1331)
(25076172373375/729, -96749554581867301262/19683)

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_u6_vm2 with specialization T=1002/1.

last edited by Alexey Pozdnyakov at 2026-06-25 23:18:47 · history