Atkin-Lehner |
2+ 3- 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
69966n |
Isogeny class |
Conductor |
69966 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
Δ |
-1578242040056967168 = -1 · 212 · 38 · 136 · 233 |
Discriminant |
Eigenvalues |
2+ 3- 0 -2 0 13+ 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,288198,-10420812] |
[a1,a2,a3,a4,a6] |
Generators |
[543:-17763:1] |
Generators of the group modulo torsion |
j |
752329532375/448524288 |
j-invariant |
L |
3.9360083770899 |
L(r)(E,1)/r! |
Ω |
0.15608172617135 |
Real period |
R |
1.0507338241276 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001766 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23322t3 414a3 |
Quadratic twists by: -3 13 |