Atkin-Lehner |
2- 3+ 7- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
47712o |
Isogeny class |
Conductor |
47712 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-182927808 = -1 · 26 · 34 · 7 · 712 |
Discriminant |
Eigenvalues |
2- 3+ 0 7- 0 2 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,142,0] |
[a1,a2,a3,a4,a6] |
Generators |
[50:360:1] |
Generators of the group modulo torsion |
j |
4913000000/2858247 |
j-invariant |
L |
5.5941434387624 |
L(r)(E,1)/r! |
Ω |
1.0847412292246 |
Real period |
R |
2.5785612679056 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000009 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
47712h1 95424y1 |
Quadratic twists by: -4 8 |