Atkin-Lehner |
13+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
61009b |
Isogeny class |
Conductor |
61009 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
Δ |
-4314548154650851 = -1 · 136 · 197 |
Discriminant |
Eigenvalues |
0 2 -3 1 -3 13+ -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-46936257,123784336522] |
[a1,a2,a3,a4,a6] |
Generators |
[2883474:30140:729] [252164:109351:64] |
Generators of the group modulo torsion |
j |
-50357871050752/19 |
j-invariant |
L |
9.8632978763458 |
L(r)(E,1)/r! |
Ω |
0.26260060042429 |
Real period |
R |
4.6950091985721 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000005 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
361b3 3211a3 |
Quadratic twists by: 13 -19 |