Atkin-Lehner |
3+ 5+ 11+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
8745b |
Isogeny class |
Conductor |
8745 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
96000 |
Modular degree for the optimal curve |
Δ |
405868431095078985 = 310 · 5 · 1110 · 53 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 2 11+ -4 4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-272316,-45414396] |
[a1,a2,a3,a4,a6] |
j |
2233280579508754319809/405868431095078985 |
j-invariant |
L |
0.84642979824215 |
L(r)(E,1)/r! |
Ω |
0.21160744956054 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
26235m1 43725o1 96195e1 |
Quadratic twists by: -3 5 -11 |