Atkin-Lehner |
2- 3+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69312ca |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
583680 |
Modular degree for the optimal curve |
Δ |
35686677872775168 = 212 · 33 · 199 |
Discriminant |
Eigenvalues |
2- 3+ 0 0 -2 6 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-228633,41161113] |
[a1,a2,a3,a4,a6] |
j |
1000000/27 |
j-invariant |
L |
0.73086674819874 |
L(r)(E,1)/r! |
Ω |
0.36543336743725 |
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 |
69312cw1 34656m1 69312cx1 |
Quadratic twists by: -4 8 -19 |