Atkin-Lehner |
2- 31+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
23312k |
Isogeny class |
Conductor |
23312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
56448 |
Modular degree for the optimal curve |
Δ |
12515534700544 = 233 · 31 · 47 |
Discriminant |
Eigenvalues |
2- -1 -3 1 -6 -4 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-10432,-369664] |
[a1,a2,a3,a4,a6] |
Generators |
[416:8192:1] |
Generators of the group modulo torsion |
j |
30655480635073/3055550464 |
j-invariant |
L |
2.1586204832112 |
L(r)(E,1)/r! |
Ω |
0.47542593616651 |
Real period |
R |
1.1350981924844 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2914f1 93248ba1 |
Quadratic twists by: -4 8 |