Atkin-Lehner |
2+ 3+ 13- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117312o |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
272896 |
Modular degree for the optimal curve |
Δ |
-31920336175104 = -1 · 215 · 313 · 13 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 3 -3 -2 13- -2 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-449,272001] |
[a1,a2,a3,a4,a6] |
j |
-306182024/974131353 |
j-invariant |
L |
1.0567696466988 |
L(r)(E,1)/r! |
Ω |
0.52838477975848 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312bl1 58656t1 |
Quadratic twists by: -4 8 |