Atkin-Lehner |
2+ 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312p |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
6937197428736 = 214 · 32 · 196 |
Discriminant |
Eigenvalues |
2+ 3+ 2 0 -4 -2 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-6257,-140175] |
[a1,a2,a3,a4,a6] |
j |
35152/9 |
j-invariant |
L |
1.0938592617845 |
L(r)(E,1)/r! |
Ω |
0.54692963645877 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
69312dl2 8664g2 192c2 |
Quadratic twists by: -4 8 -19 |