Atkin-Lehner |
3- 11- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
24321o |
Isogeny class |
Conductor |
24321 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
9216 |
Modular degree for the optimal curve |
Δ |
-8828523 = -1 · 32 · 114 · 67 |
Discriminant |
Eigenvalues |
-2 3- -4 2 11- -4 -3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-40,160] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:16:1] |
Generators of the group modulo torsion |
j |
-495616/603 |
j-invariant |
L |
2.2060072270666 |
L(r)(E,1)/r! |
Ω |
2.0954472464159 |
Real period |
R |
0.17546033277938 |
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 |
72963p1 24321n1 |
Quadratic twists by: -3 -11 |