Atkin-Lehner |
2+ 3- 13- 47- |
Signs for the Atkin-Lehner involutions |
Class |
117312bl |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
26 |
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 |
7.7594188028152 |
L(r)(E,1)/r! |
Ω |
0.29843917991594 |
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 |
117312o1 58656d1 |
Quadratic twists by: -4 8 |