Atkin-Lehner |
2+ 3- 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117312x |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-120127488 = -1 · 216 · 3 · 13 · 47 |
Discriminant |
Eigenvalues |
2+ 3- -2 -1 -3 13+ 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,31,-513] |
[a1,a2,a3,a4,a6] |
Generators |
[9:24:1] [27:144:1] |
Generators of the group modulo torsion |
j |
48668/1833 |
j-invariant |
L |
12.356600419622 |
L(r)(E,1)/r! |
Ω |
0.89581746392121 |
Real period |
R |
3.4484146927259 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000001033 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312bw1 14664a1 |
Quadratic twists by: -4 8 |