Atkin-Lehner |
2- 13+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
55744h |
Isogeny class |
Conductor |
55744 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-489533997056 = -1 · 223 · 13 · 672 |
Discriminant |
Eigenvalues |
2- -1 -3 3 -4 13+ 1 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2497,59489] |
[a1,a2,a3,a4,a6] |
Generators |
[37:128:1] [-5:268:1] |
Generators of the group modulo torsion |
j |
-6570725617/1867424 |
j-invariant |
L |
7.146756081372 |
L(r)(E,1)/r! |
Ω |
0.88415467035672 |
Real period |
R |
1.0103939278083 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999972 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
55744d1 13936c1 |
Quadratic twists by: -4 8 |