Atkin-Lehner |
13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
61009a |
Isogeny class |
Conductor |
61009 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
47040 |
Modular degree for the optimal curve |
Δ |
-33107082931 = -1 · 136 · 193 |
Discriminant |
Eigenvalues |
0 0 1 -3 5 13+ -7 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-6422,198279] |
[a1,a2,a3,a4,a6] |
Generators |
[39:84:1] |
Generators of the group modulo torsion |
j |
-884736 |
j-invariant |
L |
3.6139552670971 |
L(r)(E,1)/r! |
Ω |
1.162249459139 |
Real period |
R |
0.77736221742065 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000244 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
361a1 61009a2 |
Quadratic twists by: 13 -19 |