Atkin-Lehner |
3- 13- 103+ |
Signs for the Atkin-Lehner involutions |
Class |
52221i |
Isogeny class |
Conductor |
52221 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
516672 |
Modular degree for the optimal curve |
Δ |
-21499021199352177 = -1 · 39 · 139 · 103 |
Discriminant |
Eigenvalues |
1 3- 2 -1 -5 13- -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-326850,72241249] |
[a1,a2,a3,a4,a6] |
Generators |
[521:6330:1] |
Generators of the group modulo torsion |
j |
-364147304221/2027349 |
j-invariant |
L |
8.5431473595286 |
L(r)(E,1)/r! |
Ω |
0.38447744410005 |
Real period |
R |
1.234452904939 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999735 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
52221j1 |
Quadratic twists by: 13 |