Atkin-Lehner |
5+ 31+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
47275b |
Isogeny class |
Conductor |
47275 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-3693359375 = -1 · 59 · 31 · 61 |
Discriminant |
Eigenvalues |
-1 1 5+ -3 0 -5 2 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-1813,-30008] |
[a1,a2,a3,a4,a6] |
Generators |
[87:644:1] |
Generators of the group modulo torsion |
j |
-42180533641/236375 |
j-invariant |
L |
2.7781657111169 |
L(r)(E,1)/r! |
Ω |
0.36569864514041 |
Real period |
R |
1.8992179408018 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000024 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9455c1 |
Quadratic twists by: 5 |