curve #233

y² + xy = x³ − 47059713436231131280063000x + 124291234348538980027099166608538874432

a-invariants: [1, 0, 0, -47059713436231131280063000, 124291234348538980027099166608538874432]
rank (lower bound): ≥ 18
conductor (N): 70641518626311939848441607050541661411730955138276481056543606910
naive height: 188.9545
Faltings height: 13.4743
discriminant (Δ): -3639993566490641216689747626786054555892020902459466267407640882904268800000
primes of bad reduction: 2, 5, 17, 37, 2021179, 81005178314881, 21895530395507809193, 3132826558949676690397
regulator: 536817729199543216.84665489380964481059698918907148197929007350386929801579
submitted by: Alexey Pozdnyakov
last updated: 2026-07-01 22:32:40

Witness: 18 independent points

(3239722194224, 2415430462344812008)
(4499331922864, -1907457031091338392)
(3810007955424, -547760266366600392)
(3801947170944, 573657108993519768)
(4147838533344, 675939614911732968)
(2114906977904, -5850124186730281752)
(3404042813824, 1882105246884763368)
(3609942938544, 1204989598722206568)
(-7870624775696, 2668538857551716648)
(30495110821168/9, 52200598495644293240/27)
(-7193257748656, -9518581173018943032)
(10392518468734, -27525637468970450962)
(-2527343490552, 15069307033302071976)
(32676952036364, -182971116416499646472)
(-53350585659884/9, -376989394300296149464/27)
(249957736105436/49, -1413152923399194615756/343)
(23070911278207024/5041, 782238092196844207958488/357911)
(62220901060271384/7921, 10905936898001708604261312/704969)

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_vm4 with specialization T=2623/2.

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