curve #413

y² + xy = x³ − 6128282860470603511303288155661829055x + 5852434608243230932760773539506370894306070621155215001

a-invariants: [1, 0, 0, -6128282860470603511303288155661829055, 5852434608243230932760773539506370894306070621155215001]
c-invariants: [294157577302588968542557831471767794641, -5056503501522151526346544704087387905494281763885757452825]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 13999135026628284722798542160932926594351569117651995795466833665069304457492423676119108886
discriminant (Δ): -66643924316290495097031601682555186588559481494004949405963419708479467342166011289207729989773885624388026368
Faltings height: 19.9486
naive height: 265.7361
primes of bad reduction: 2, 3, 7, 11, 13, 31, 71, 216228942283, 41321404328989, 118524173442917815776414453724717264619387885840363991228263
regulator: 18396873238818635773896037.742152104513935899901041838124032178326846823470906769759763
submitted by: Rayan Hatout
submitted at: 2026-08-29 00:44:39 UTC
last updated: 2026-08-29 00:44:39 UTC

(2151837540602413926, 1621494485175430398778624941)
(384455577965177358, 1884995213460540972203183829)
(38242131294975462406/9, 203004898697114448450273056927/27)
(187731278164711501206/169, 1416410698873224116903086903857/2197)
(-969545969988423786, 3298892928315569428236054861)
(458509810273858374, 1771708182670860389095436781)
(1028192489565669030, 798977172582268206170620461)
(1726765414118345870, 647345816581646430785433941)
(340472081873041710558, 6282186304016483262997843439013)
(57974946869381326998, 441032695543768221343013914653)
(420525477987360294, 1830219101459878206901050285)
(968826584430375702, 908050692570304025630351949)
(-2752055532080721696, 1369037840805705305277126555)
(4698869364285560979/4, 4191407432190711302631776103/8)
(1549776865258801728, 277903930800277253261883333)
(1427778350895660938, 114908764972973081289935669)
(3138026425577083110, 4185991609591963343895144621)
(1433853991245920730, 115263293745335490298149909)
(1390570919539384614, -139829382733652460345256275)
(23178358146012493846/9, 72202171342405731417309760895/27)
(149234398498519731334/81, 658363414747778027582503237669/729)
(1422721978314185580, 115660138309197699562970109)
(1139136548975660838, -591323723834291753844730707)
(1482647435991245478, -159911562773787534911891667)

rank-17 K3 fibration (arXiv:2608.25406), specialized at t = -288/65

last edited by NDElkies at 2026-08-29 01:42:28 UTC · history