Atkin-Lehner |
3+ 5+ 13+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
78585b |
Isogeny class |
Conductor |
78585 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
Δ |
-1.0220279839958E+20 |
Discriminant |
Eigenvalues |
-1 3+ 5+ -2 2 13+ 7 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-648277749961,-200904827131421782] |
[a1,a2,a3,a4,a6] |
Generators |
[288307536703305092538268802737967677497755617158334197004457901869110668084367363401015088291765178169975526004100413641033880910860831001379057529112570513126810930665783233522931531199781737494810736186259906743703055616304212550249099736428422518678896447374211783071290245210938073466868337698810673433032088785305101886366396181318671599532894211369131588841767841685416:-36538822157410434882711291565399093383789265730672196257592591303468648406791777379480078321241182146378029636561737707260335574755338344785871214875041920957323038971689357845025986339619293102279705680696901081257751033206376411774675698652086480248925412369039600062432153822219883577573278637270136051222016963279239307273309578675083740617798147703946010282873271361539974:307746928811417750051524432512039735469291781738546068550835940875184669724168557633967023121277185618953134080428022433018484889195508846854583699027752328994103383913180160470306475754574466602300773227360706735400367523368787726031692093828676407576724572679699118091299880769623136333796106805337653010877428807953600251613035125874830382218552354589262056919969747] |
Generators of the group modulo torsion |
j |
-218561436977626127589484337161/741360195 |
j-invariant |
L |
3.0644344633429 |
L(r)(E,1)/r! |
Ω |
0.0026602918256782 |
Real period |
R |
575.95832791044 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78585g2 |
Quadratic twists by: 13 |