Atkin-Lehner |
2+ 3+ 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
47424f |
Isogeny class |
Conductor |
47424 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
319488 |
Modular degree for the optimal curve |
Δ |
-9316663226597376 = -1 · 216 · 313 · 13 · 193 |
Discriminant |
Eigenvalues |
2+ 3+ 1 3 6 13+ -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-43265,-5779071] |
[a1,a2,a3,a4,a6] |
Generators |
[2283832590625:-131250106807924:688465387] |
Generators of the group modulo torsion |
j |
-136667088859396/142160998941 |
j-invariant |
L |
6.6807956988162 |
L(r)(E,1)/r! |
Ω |
0.15891882798224 |
Real period |
R |
21.019522304691 |
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 |
47424de1 5928n1 |
Quadratic twists by: -4 8 |