Atkin-Lehner |
3- 7- 73+ |
Signs for the Atkin-Lehner involutions |
Class |
32193d |
Isogeny class |
Conductor |
32193 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-169045024491 = -1 · 39 · 76 · 73 |
Discriminant |
Eigenvalues |
0 3- -3 7- 0 4 3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,1176,12262] |
[a1,a2,a3,a4,a6] |
Generators |
[70:661:1] |
Generators of the group modulo torsion |
j |
2097152/1971 |
j-invariant |
L |
3.5332170989219 |
L(r)(E,1)/r! |
Ω |
0.66720472327519 |
Real period |
R |
0.66194396106375 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10731b1 657c1 |
Quadratic twists by: -3 -7 |