Atkin-Lehner |
3- 7- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
117117ca |
Isogeny class |
Conductor |
117117 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
6050304 |
Modular degree for the optimal curve |
Δ |
3.1665623776974E+19 |
Discriminant |
Eigenvalues |
1 3- 0 7- 11- 13- -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-27151227,54460431000] |
[a1,a2,a3,a4,a6] |
Generators |
[-332172:15249825:64] |
Generators of the group modulo torsion |
j |
1382084250541230782125/19771083137421 |
j-invariant |
L |
8.9885993786891 |
L(r)(E,1)/r! |
Ω |
0.19013130008095 |
Real period |
R |
3.9396456484061 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999897789 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
39039y1 117117z1 |
Quadratic twists by: -3 13 |