Atkin-Lehner |
2+ 3- 11- 59- |
Signs for the Atkin-Lehner involutions |
Class |
11682i |
Isogeny class |
Conductor |
11682 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
195840 |
Modular degree for the optimal curve |
Δ |
-2002089510788235264 = -1 · 215 · 323 · 11 · 59 |
Discriminant |
Eigenvalues |
2+ 3- -1 -2 11- -4 5 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,299565,25456437] |
[a1,a2,a3,a4,a6] |
j |
4078200565293477839/2746350494908416 |
j-invariant |
L |
0.65938166148188 |
L(r)(E,1)/r! |
Ω |
0.16484541537047 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
93456z1 3894m1 128502bx1 |
Quadratic twists by: -4 -3 -11 |