Atkin-Lehner |
2+ 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312s |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
10676346842824704 = 214 · 36 · 197 |
Discriminant |
Eigenvalues |
2+ 3+ -2 0 -2 2 6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-133329,-18022671] |
[a1,a2,a3,a4,a6] |
j |
340062928/13851 |
j-invariant |
L |
2.0037703093223 |
L(r)(E,1)/r! |
Ω |
0.25047128907177 |
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 |
69312dn2 4332c2 3648q2 |
Quadratic twists by: -4 8 -19 |