Atkin-Lehner |
3+ 7- 17- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
13209c |
Isogeny class |
Conductor |
13209 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
16896 |
Modular degree for the optimal curve |
Δ |
-2398744083771 = -1 · 34 · 7 · 174 · 373 |
Discriminant |
Eigenvalues |
0 3+ 1 7- -5 1 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,3345,-4201] |
[a1,a2,a3,a4,a6] |
Generators |
[3:76:1] |
Generators of the group modulo torsion |
j |
4137921410269184/2398744083771 |
j-invariant |
L |
3.2924490925208 |
L(r)(E,1)/r! |
Ω |
0.48488361343895 |
Real period |
R |
0.84877303575225 |
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 |
39627f1 92463f1 |
Quadratic twists by: -3 -7 |