Atkin-Lehner |
3- 23- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
74589i |
Isogeny class |
Conductor |
74589 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
194304 |
Modular degree for the optimal curve |
Δ |
-4320723492243 = -1 · 33 · 237 · 47 |
Discriminant |
Eigenvalues |
0 3- 0 4 0 2 3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-118143,-15669808] |
[a1,a2,a3,a4,a6] |
Generators |
[32516:477655:64] |
Generators of the group modulo torsion |
j |
-1231925248000/29187 |
j-invariant |
L |
8.3650502378931 |
L(r)(E,1)/r! |
Ω |
0.12875575109702 |
Real period |
R |
5.4140301604952 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000688 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3243c1 |
Quadratic twists by: -23 |