curve #215

y² + xy = x³ − x² − 50968883660167848001767x + 5184551861194511414139157441329641

a-invariants: [1, -1, 0, -50968883660167848001767, 5184551861194511414139157441329641]
rank (lower bound): ≥ 18
conductor (N): 5692233049957592618627388003164315988519877481788141693279603950
naive height: 168.7851
Faltings height: 12.0564
discriminant (Δ): -3137843468789122931018347636744329188671582461835713108420381677437500
primes of bad reduction: 2, 3, 5, 7, 1641821, 6169133, 19823469628629700195532996237768951332198248209
regulator: 637156633527749476.44719296654871370884618117594544024639322389824847313621
submitted by: RoyManami
last updated: 2026-07-01 22:31:42

Witness: 18 independent points

(124382151439, 27735090940849243)
(139856705149, -28138915164057362)
(46552881319, 53969333884318678)
(-208337990336, 82222089599352493)
(-61208135681, 89860755353561878)
(51849193319, -51780761335278122)
(138959488114, -28021728457973057)
(-159455928961, -96215746848427157)
(-54052543061, 88213549492595743)
(913563564151/4, -590980570363245601/8)
(120995404208, 28087487052518733)
(79772580818, 40327102621276359)
(-168653863876, 94781091428093613)
(-763198531, -72273444214523922)
(-981027959149/4, -433225119414961251/8)
(14219450798539, 53612964608312831743)
(5762465089339/36, 7252249875034931683/216)
(1114322441480, -1154149212334190531)

Commentary

Rank-18 naive-height record: h=168.785 (beats prior r18 height record 173.853). Found via Mestre/Fermigier quartic family, sextuple mestre_ais(u=-6,v=-4), specialization T=962; certified by hyperellratpoints + Neron-Tate height-pairing independence (18 independent points).

last edited by RoyManami at 2026-06-25 20:55:28 · history