Atkin-Lehner |
2- 3+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
122304fl |
Isogeny class |
Conductor |
122304 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
921600 |
Modular degree for the optimal curve |
Δ |
-43953678742192128 = -1 · 228 · 32 · 72 · 135 |
Discriminant |
Eigenvalues |
2- 3+ -2 7- 3 13+ -5 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-130209,20750913] |
[a1,a2,a3,a4,a6] |
Generators |
[93:3072:1] |
Generators of the group modulo torsion |
j |
-19007021070457/3421836288 |
j-invariant |
L |
4.0090495161008 |
L(r)(E,1)/r! |
Ω |
0.34633419685275 |
Real period |
R |
1.4469584681316 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999998118846 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122304dk1 30576da1 122304gr1 |
Quadratic twists by: -4 8 -7 |