Atkin-Lehner |
2- 3+ 37- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
83472m |
Isogeny class |
Conductor |
83472 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
16128 |
Modular degree for the optimal curve |
Δ |
-128212992 = -1 · 213 · 32 · 37 · 47 |
Discriminant |
Eigenvalues |
2- 3+ 0 -1 4 -2 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-48,576] |
[a1,a2,a3,a4,a6] |
Generators |
[0:24:1] |
Generators of the group modulo torsion |
j |
-3048625/31302 |
j-invariant |
L |
5.8526324143853 |
L(r)(E,1)/r! |
Ω |
1.5796289188897 |
Real period |
R |
0.46313348853709 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999822 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10434j1 |
Quadratic twists by: -4 |