Atkin-Lehner |
3- 11+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
3069a |
Isogeny class |
Conductor |
3069 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
Δ |
4.1064542595012E+20 |
Discriminant |
Eigenvalues |
-1 3- 2 -2 11+ 4 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-2245289,852825138] |
[a1,a2,a3,a4,a6] |
j |
1717167849316307276617/563299624074237039 |
j-invariant |
L |
1.2410220760309 |
L(r)(E,1)/r! |
Ω |
0.15512775950386 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
49104bs2 1023a2 76725o2 33759i2 |
Quadratic twists by: -4 -3 5 -11 |