Atkin-Lehner |
7- 13+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
72163g |
Isogeny class |
Conductor |
72163 |
Conductor |
∏ cp |
30 |
Product of Tamagawa factors cp |
deg |
2056320 |
Modular degree for the optimal curve |
Δ |
3111906383982939907 = 75 · 138 · 613 |
Discriminant |
Eigenvalues |
-1 3 0 7- -3 13+ 7 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-391605,41249290] |
[a1,a2,a3,a4,a6] |
Generators |
[-3318:254216:27] |
Generators of the group modulo torsion |
j |
1375964544515625/644712973723 |
j-invariant |
L |
7.7108701097546 |
L(r)(E,1)/r! |
Ω |
0.22570692695265 |
Real period |
R |
1.1387732184107 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001363 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5551a1 |
Quadratic twists by: 13 |