Atkin-Lehner |
2+ 13+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
83824c |
Isogeny class |
Conductor |
83824 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-153222224896 = -1 · 210 · 136 · 31 |
Discriminant |
Eigenvalues |
2+ 2 -2 0 2 13+ 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,1296,5264] |
[a1,a2,a3,a4,a6] |
Generators |
[190274:4486950:343] |
Generators of the group modulo torsion |
j |
48668/31 |
j-invariant |
L |
8.9236698894188 |
L(r)(E,1)/r! |
Ω |
0.63894560465275 |
Real period |
R |
6.9831217428389 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000824 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
41912d1 496c1 |
Quadratic twists by: -4 13 |