Atkin-Lehner |
2- 7- 13+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
68432o |
Isogeny class |
Conductor |
68432 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
16128 |
Modular degree for the optimal curve |
Δ |
-245260288 = -1 · 213 · 72 · 13 · 47 |
Discriminant |
Eigenvalues |
2- 0 -2 7- -4 13+ 3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-251,1706] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:56:1] [5:24:1] |
Generators of the group modulo torsion |
j |
-426957777/59878 |
j-invariant |
L |
8.8694776011212 |
L(r)(E,1)/r! |
Ω |
1.6987941000108 |
Real period |
R |
0.65263041597526 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999442 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8554j1 |
Quadratic twists by: -4 |