Atkin-Lehner |
2+ 3+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
4416f |
Isogeny class |
Conductor |
4416 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
10752 |
Modular degree for the optimal curve |
Δ |
-238364196139008 = -1 · 212 · 314 · 233 |
Discriminant |
Eigenvalues |
2+ 3+ -2 2 2 2 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,10391,-624407] |
[a1,a2,a3,a4,a6] |
Generators |
[291:5192:1] |
Generators of the group modulo torsion |
j |
30289632400448/58194383823 |
j-invariant |
L |
3.008905348363 |
L(r)(E,1)/r! |
Ω |
0.29075077080344 |
Real period |
R |
5.1743720920299 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4416m1 2208d1 13248s1 110400dz1 |
Quadratic twists by: -4 8 -3 5 |