Atkin-Lehner |
2- 3+ 13+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
9672f |
Isogeny class |
Conductor |
9672 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
13824 |
Modular degree for the optimal curve |
Δ |
-9265882159872 = -1 · 28 · 312 · 133 · 31 |
Discriminant |
Eigenvalues |
2- 3+ 0 2 1 13+ 4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,4287,97461] |
[a1,a2,a3,a4,a6] |
j |
34028506496000/36194852187 |
j-invariant |
L |
1.9327283647197 |
L(r)(E,1)/r! |
Ω |
0.48318209117992 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
19344e1 77376t1 29016b1 125736d1 |
Quadratic twists by: -4 8 -3 13 |