Atkin-Lehner |
2+ 3- 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
85176x |
Isogeny class |
Conductor |
85176 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
1204224 |
Modular degree for the optimal curve |
Δ |
322767327709008 = 24 · 38 · 72 · 137 |
Discriminant |
Eigenvalues |
2+ 3- 4 7+ 6 13+ -6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-321438,70139225] |
[a1,a2,a3,a4,a6] |
j |
65239066624/5733 |
j-invariant |
L |
4.1478009739068 |
L(r)(E,1)/r! |
Ω |
0.51847512837561 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
28392v1 6552ba1 |
Quadratic twists by: -3 13 |