Atkin-Lehner |
2- 3- 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
122304ib |
Isogeny class |
Conductor |
122304 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-208039104 = -1 · 26 · 36 · 73 · 13 |
Discriminant |
Eigenvalues |
2- 3- -1 7- -2 13- -2 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,19,-687] |
[a1,a2,a3,a4,a6] |
Generators |
[16:63:1] |
Generators of the group modulo torsion |
j |
32768/9477 |
j-invariant |
L |
6.7707538801905 |
L(r)(E,1)/r! |
Ω |
0.8361721303493 |
Real period |
R |
0.67477672062388 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000035831 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122304bt1 30576bo1 122304ez1 |
Quadratic twists by: -4 8 -7 |