Atkin-Lehner |
2+ 3+ 13- 43- |
Signs for the Atkin-Lehner involutions |
Class |
13416a |
Isogeny class |
Conductor |
13416 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
8192 |
Modular degree for the optimal curve |
Δ |
-27733313712 = -1 · 24 · 3 · 132 · 434 |
Discriminant |
Eigenvalues |
2+ 3+ 2 0 0 13- -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-447,-8652] |
[a1,a2,a3,a4,a6] |
Generators |
[1059036:1934920:35937] |
Generators of the group modulo torsion |
j |
-618724784128/1733332107 |
j-invariant |
L |
4.5736824822898 |
L(r)(E,1)/r! |
Ω |
0.48119818380895 |
Real period |
R |
9.5047791870006 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
26832j1 107328q1 40248u1 |
Quadratic twists by: -4 8 -3 |