curve #4542

y² + xy + y = x³ − x² − 1479084443271286193697833757x + 22301974944464416735224376553466227524389

a-invariants: [1, -1, 1, -1479084443271286193697833757, 22301974944464416735224376553466227524389]
c-invariants: [70996053277021737297496020321, -19268906352016936576994114744376981848980881]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 954008727620351754173693616590312149665613897220815618084790 ★ record for rank ≥ 20
discriminant (Δ): -7777450796666578180999764354632694464167804699619784251470975166374995944960000000
Faltings height: 14.5029
naive height: 199.3341
primes of bad reduction: 2, 5, 7, 11, 23, 31, 163, 17597663263839156564907567, 86542900242116937796191257
regulator: 238455863323517366.567279765620928105809103134206534513020925182124767140200939
submitted by: Matej Jurasić
submitted at: 2026-10-17 12:11:33 UTC
last updated: 2026-10-17 12:11:33 UTC

(20892892311447, -22795645786289560224)
(25859511276447, 36690581137697764776)
(20845335496647, -22974902996127607224)
(6877490526447, 111601475703512764776)
(35288749242287, 118540553262845797736)
(31768317674447, -85879948967765939224)
(12893585029047, -73312774477805711224)
(25447770603247, 33797477954834519976)
(24716230892047, 29043606146478508776)
(24596916195777, 28326599990154458876)
(178407054215023/9, -749976683331265051048/27)
(281369913519, 147938593060536556392)
(-35770989865553, 171578072598298300776)
(95456250645527, 866545697013745808096)
(15035183058447, 58842782118219904776)
(35784574826863, 123276078748252666728)
(22280188519613, -20192381204829360292)
(224814364122347, -3324490652623806365624)
(-44340874564803, -26583729106462722724)
(27969820581947, -53040969187847759224)

Specialization at T = -23/2 of a rank-16 fibration of X1008 (two neighbour steps from the one in curve#751).

last edited by Matej Jurasić at 2026-10-17 12:11:33 UTC · history