curve #232

y² + xy = x³ + x² − 31972892142603899925x + 73862336294883442290824915625

a-invariants: [1, 1, 0, -31972892142603899925, 73862336294883442290824915625]
c-invariants: [1534698822844987196425, -63817058570289535310610131073125]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 1909993724175983557195812136598184923916762977783755050
discriminant (Δ): -265011629229417718560918933952998158193450863167496013187500
Faltings height: 10.1515
naive height: 146.4671
primes of bad reduction: 2, 3, 5, 37, 58417, 1055716357, 1519100351, 3673381145443713464969597689
regulator: 16048137292672682.3031590987077593193953077608954805380268070422691776228
submitted by: Alexey Pozdnyakov
submitted at: 2026-06-25 23:18:49 UTC
last updated: 2026-07-01 22:33:42 UTC

Witness: 17 independent points log in to add more points →

(2664945425, 87076738827325)
(-342974200, -291183394150925)
(149881895, 262818390289590)
(7129560785, -456413221223630)
(-2712349675, -375004877470550)
(3147196470, 66405189566265)
(4745840670, 170334561592365)
(4757680200, -171577755782925)
(36110154700, -6782709964999925)
(-3062083040, -378224349847955)
(-5946513290, -231761534756255)
(3130864116, -66704313496629)
(6582355515/4, 1282598116599585/8)
(29221163254, -4908256494503999)
(3272296319, -65400846476570)
(-6204206346, -182795562231999)
(6065244854, -321036150563855)

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_vm6 with specialization T=1368/1.

last edited by Alexey Pozdnyakov at 2026-06-25 23:18:49 UTC · history