Atkin-Lehner |
2- 3+ 7- 47- |
Signs for the Atkin-Lehner involutions |
Class |
63168cs |
Isogeny class |
Conductor |
63168 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
57344 |
Modular degree for the optimal curve |
Δ |
-37439926272 = -1 · 212 · 34 · 74 · 47 |
Discriminant |
Eigenvalues |
2- 3+ 0 7- -6 0 -2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1113,17433] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:168:1] [-3:144:1] |
Generators of the group modulo torsion |
j |
-37259704000/9140607 |
j-invariant |
L |
8.8328847048533 |
L(r)(E,1)/r! |
Ω |
1.1002147983999 |
Real period |
R |
1.0035409355641 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999904 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
63168cu1 31584bb1 |
Quadratic twists by: -4 8 |