curve #224

y² + xy + y = x³ − 6673066689650959455557789303x + 209378639414088313855940823602467379072006

a-invariants: [1, 0, 1, -6673066689650959455557789303, 209378639414088313855940823602467379072006]
c-invariants: [320307201103246053866773886521, -180903144453772783632334526461612615679043181]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 572909165125068318062716813219644563458478178791019281490
discriminant (Δ): 79001812652238926310614069141452885179698753918710242185753213892099337491708562500
Faltings height: 14.7857
naive height: 203.8172
primes of bad reduction: 2, 3, 5, 7, 17, 19, 23, 29, 510907, 5615780176703, 4413530848208303762736531936829
regulator: 4448647520751208.6688351763983694041782506910401027616687954510865258321494
submitted by: Alexey Pozdnyakov
submitted at: 2026-06-25 23:18:40 UTC
last updated: 2026-07-01 22:33:40 UTC

Witness: 18 independent points log in to add more points →

(52648439943435, 63135542408283779122)
(152427780121155, -1653408591206197043978)
(33382358374155, 154326358334583163522)
(39388005269550, 87447073241685904477)
(295951840628325, 4914890668196834574952)
(50025489363555, -27321818658715172978)
(154944573237195/4, 759491082898156748051/8)
(-78057807129435, 504634277034685447912)
(39508640005905, -86053348519378572728)
(-71995604329495, 562699303600646341272)
(89282248783980, -570341705230530251603)
(-49554040294920, 646816080171094290397)
(93798472814837, -639303212109997850622)
(36963847321485, 114982967705704135642)
(548034406500745/9, -4583878846330509251656/27)
(199544434564695/4, 201286633741255673801/8)
(44390697022770, 25098478885753929757)
(3862239457538245/144, 385208152479162663358691/1728)

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 sextuple_A_m498_m216_m6_414_552_m246 with specialization T=966/145.

last edited by Alexey Pozdnyakov at 2026-06-25 23:18:40 UTC · history