curve #148

y² + xy = x³ − 80634779807196097636x + 278711474435456966031090976016

a-invariants: [1, 0, 0, -80634779807196097636, 278711474435456966031090976016]
rank (lower bound): ≥ 15
conductor (N): 38802091035979009024912187041902860425470 ★ record for rank ≥ 15
naive height: 149.1231
Faltings height: 10.1032
discriminant (Δ): -3574107331245376801878879599917457045580677964135913881600
primes of bad reduction: 2, 3, 5, 7, 17, 47, 67, 5659, 33260111, 104050049, 176241660609479
regulator: 154592244929.63709013408067677511651316763074973030093853274937906167
submitted by: Alexey Pozdnyakov
last updated: 2026-07-01 22:42:37

Witness: 15 independent points

(5122119536, 8656400619572)
(5190432200, -3927406903204)
(5051647736, 16929747656492)
(5191391816, -3952015295908)
(5157438344, 5111117078108)
(5211393686, 5113496460722)
(5072480576, -14436717901348)
(-10311204664, -117707218206628)
(5692157144, 64458341314268)
(-10319795512, 108662784210140)
(5223474566, 6211821138242)
(5232768830, -7165433634934)
(3778637144, 167251374704588)
(6769000520, -207478525394596)
(6159961880, 125475448853516)

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_u5_vm2, specialization T=453/1. GP famcert certified rank >= 15. conductor record for rank 15: log N 93.459293 < 94.129755

last edited by Alexey Pozdnyakov at 2026-06-24 17:55:21 · history