curve #229

y² + xy = x³ − x² − 202989927789473297517x + 1151371062064532719495377812641

a-invariants: [1, -1, 0, -202989927789473297517, 1151371062064532719495377812641]
c-invariants: [9743516533894718280825, -994784597579910445241480197858125]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 30986346452249226528045018007683724606761684860484150
discriminant (Δ): -37375459960171559857395780326960541388085635113973452493687500
Faltings height: 10.5826
naive height: 151.9602
primes of bad reduction: 2, 3, 5, 11, 19, 12163, 26992182881, 4165307236463, 240927190974505105687
regulator: 10448212595552444.6828230115365136877253067334401168356078834148626238197
submitted by: Alexey Pozdnyakov
submitted at: 2026-06-25 23:18:46 UTC
last updated: 2026-07-01 22:34:39 UTC

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

(7037990894, -267108038594947)
(10351315964, -399127987283707)
(9989176439, -347028484970332)
(8568582824, 202839608620313)
(7399727885, -233413493097169)
(16003609244, -1414777276909147)
(-8335261176, -1504734911319937)
(-6402302161, -1479370627219132)
(10572774245, -432517338548284)
(-7012120786, 1493313959892293)
(168235468049, 68764723550231588)
(24378863795/4, 2999674420649533/8)
(8862082769, 220119583035428)
(213351414551/4, 95353143544380799/8)
(533117324, 1021422826196063)
(128876285, -1060760459059516)
(5035853549, -506808060708412)

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_u4_v6 with specialization T=2118/1.

last edited by Alexey Pozdnyakov at 2026-06-25 23:18:46 UTC · history