Atkin-Lehner |
3- 5- 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
47775cz |
Isogeny class |
Conductor |
47775 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
322560 |
Modular degree for the optimal curve |
Δ |
-1141700823046875 = -1 · 3 · 58 · 78 · 132 |
Discriminant |
Eigenvalues |
-2 3- 5- 7+ 4 13+ -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,14292,1491494] |
[a1,a2,a3,a4,a6] |
Generators |
[-67:487:1] |
Generators of the group modulo torsion |
j |
143360/507 |
j-invariant |
L |
3.6277820870425 |
L(r)(E,1)/r! |
Ω |
0.34658496684576 |
Real period |
R |
1.744537142912 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000005 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47775i1 47775bt1 |
Quadratic twists by: 5 -7 |