curve #5492

y² + xy + y = x³ − 7567482743367974220757760829051x + 9520944567514050512201870335806734336987734498

a-invariants: [1, 0, 1, -7567482743367974220757760829051, 9520944567514050512201870335806734336987734498]
c-invariants: [363239171681662762596372519794425, -8226096106332140187401173492631162361716182298125]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 283356624296300907327814437722760790765388919150843083033730052415550 ★ record for rank ≥ 22
discriminant (Δ): -11424711575694306593667590316802367598908473330686189632334964073621906259439820068473468187500
Faltings height: 16.7669
naive height: 225.2628
primes of bad reduction: 2, 3, 5, 11, 23, 29, 37, 47, 59, 1246665990527, 77049620549668297771, 26124704214009516495361753
regulator: 71098327539573798215.00345784017601152140497525000709259121366444469775154478903708
submitted by: Matej Jurasić
submitted at: 2026-10-22 11:58:35 UTC
last updated: 2026-10-22 11:58:35 UTC

(1025596948375067, -53277862582098900231834)
(4181610694739117, -225822433308440445813684)
(1738748143023692, 40244996485756170465666)
(5485200751202702, -364756580835919050202464)
(2678779838230817, -92042802615972729584334)
(-12891223575050857/4, -167020099232232436159047/8)
(1113099876494762, 49766469707274337864356)
(1692261775354262, 39509457550947329510481)
(-2353432190339173, 119564549238451470281286)
(3710986931541617, 180398694141631088930316)
(-387209749622683, 111324268750764088601916)
(3216508271424923, -135859592906430496446306)
(2544280910652956, -82080465302502486280974)
(-119212118381190277/169, -264627077753389334632982598/2197)
(-3124260026466583, -51650981562380929477734)
(-6247555058286457/4, 1059215977298374623403653/8)
(102867361328406281, -32980934193310965303279174)
(-1979805248969458, 129394687530175414258641)
(9333140944068977, -867109756588154355941364)
(-12393138413942377/4, -454354024644913532342127/8)
(6919493446182077, 537083713972892088251286)
(157475436893646451/81, -33856780263050921665698406/729)

Specialization at T = -27/49 of a rank-16 fibration of X1152 (two neighbour steps from the one in curve#3856).

last edited by Matej Jurasić at 2026-10-22 11:58:35 UTC · history