Atkin-Lehner |
3+ 7- 17+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
13209b |
Isogeny class |
Conductor |
13209 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
29184 |
Modular degree for the optimal curve |
Δ |
-506382060051 = -1 · 34 · 7 · 176 · 37 |
Discriminant |
Eigenvalues |
2 3+ 1 7- -3 -1 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-10080,394409] |
[a1,a2,a3,a4,a6] |
Generators |
[-806:4909:8] |
Generators of the group modulo torsion |
j |
-113278735513686016/506382060051 |
j-invariant |
L |
8.3527676987935 |
L(r)(E,1)/r! |
Ω |
0.93410222408584 |
Real period |
R |
2.2355068544473 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
39627l1 92463l1 |
Quadratic twists by: -3 -7 |