curve #146

y² + xy + y = x³ − 5556025348607281549409726x + 4850907150606399626446672370423348348

a-invariants: [1, 0, 1, -5556025348607281549409726, 4850907150606399626446672370423348348]
rank (lower bound): ≥ 18
conductor (N): 9120814589307131223357058040664717870768277440871516003950
naive height: 182.5444
Faltings height: 13.1378
discriminant (Δ): 811199414708319103053032954716768368937184231487647543973012218268927562500
primes of bad reduction: 2, 3, 5, 7, 43, 59, 109, 4289, 215507435356125127, 33984357076304424732533341601
regulator: 15766637859188658.989463949045535958988597456763312195003257509017069237721
submitted by: Alexey Pozdnyakov
last updated: 2026-07-01 22:31:43

Witness: 18 independent points

(1138306568247, -37396477182461549)
(3142973901027, -4293677880641280689)
(22836036442977, -108566183571808263089)
(5819352360516, 13022669701398455716)
(1083747051522, -320079105741957224)
(587537547102, 1337666265527601361)
(1630066809897, 354250759937068651)
(1612633529747, 291320348627899551)
(12987694770903/4, -36696958747221394507/8)
(-1913451133473, -2911421483283008939)
(4714344382032, 9134240722855240396)
(720443413816947, -19337374121787475106099)
(6113245803303, -14119082368348176203)
(135656188487163/4, -1576286240662244845417/8)
(85928392099863/4, -791921937724290050467/8)
(10939779827704557/16, -1144222024948804078791071/64)
(437151064634118/169, -6130650012875911790528/2197)
(45869362770434967/3721, 9655585436888094099575191/226981)

Commentary

Generated with assistance from OpenAI Codex, based on GPT-5. Method: generalized Mestre/Fermigier quartic-family search, sieving Mestre (u,v) families by Mestre-Nagao score, rescoring survivors, exact-height triaging the best candidates, and certifying top score/height candidates with GP famcert. This hit came from family mestre_u2_vm4, specialization T=826/9. GP famcert certified rank >= 18. conductor record for rank 18: log N 133.457909 < 138.988198 naive-height record for rank 18: h 182.544379 < 190.774340

last edited by Alexey Pozdnyakov at 2026-06-24 03:58:15 · history