curve #478

y² + xy + y = x³ − x² − 142439622805746929644754975203567774592x + 564187004933212877252354468248101698569580185650481725859

a-invariants

[1, -1, 1, -142439622805746929644754975203567774592, 564187004933212877252354468248101698569580185650481725859]

rank (lower bound)

≥ 23

torsion subgroup

trivial

conductor (N)

1360557294466858957741722599715063415022237961323147559730598444799359081503776406464712530

discriminant (Δ)

47449087255916637600139677497241873824093865742792955565616957556445552915357232868943917951693031362922319872000000

Faltings height

20.9207

naive height

275.1695

primes of bad reduction

2, 3, 5, 7, 11, 13, 29, 61, 197, 241, 13763, 86172409, 21659566612934585385435706416828480983688636674500021395911792461

regulator

1091370852702175779700021.60876259792802061730550450030041179024372246290727405380689

submitted by

Alexandar Slavov

submitted at

2026-09-01 05:40:29 UTC

later contributions

rank ≥ 21 → ≥ 23 · Bhavik Mehta · 2026-09-06 15:47:54 UTC

Witness: 23 independent points log in to add more points →

(44178634810723071997, -283720157535840058618386491359)
(37556151298128041917, 219513829055713026686373031841)
(4531998596384869717, -3425434951195807402887785959)
(-392491249213547783, -24900458778546605240332708759)
(3817014065041472017, 8723836054617381173733590741)
(15027497696945032637, 42629460381351799095168418721)
(4082855873946308797, 7119451254283056720936134561)
(21358074147808957897, 85233835203080175459399181961)
(17009262857476509727, 55339220200713258967046220431)
(-13546967822749782083, 2769095351067495413779726241)
(-4066416780105500483, -32804948474930336044652401759)
(18855627889954726117, -67692160150780050306917822359)
(72070318368890271677, 603855262184167709161975224481)
(3772048660181036823601/289, 149710404225612602762163703488709/4913)
(-12956825580564836633, 15315651064514907705485196641)
(67677098939688270799, 548541921301944075837007403057)
(-8545147369314041603, -34020461668806261467532811039)
(1244943557649931477, -19717688324633720846780845159)
(-49476846306694736033/4, -166583684439764889696186102761/8)
(-13045637477728614083, 14219112561975217995340126241)
(9082769310254737897, -4442887608209781348468335539)
(199665124135355137597, 2816381739975806203011438057761)
(-119243876338916702477/9, 302557027775532503827015581347/27)

Commentary

This curve was found by Aleksandar Lyubomirov Slavov, a 17-year-old independent researcher and high-school student from Bulgaria, by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at (t=106). The seventeen generic sections specialize to independent rational points, and three additional independent rational points were found computationally. Exact arithmetic and the ICARM verifier certify the displayed 20 rational points as independent, establishing rank≥20.

last edited by Alexandar Slavov at 2026-09-01 05:40:29 UTC · history