Atkin-Lehner |
3- 11- 83- |
Signs for the Atkin-Lehner involutions |
Class |
8217m |
Isogeny class |
Conductor |
8217 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
6912 |
Modular degree for the optimal curve |
Δ |
-2174440059 = -1 · 39 · 113 · 83 |
Discriminant |
Eigenvalues |
-2 3- -1 0 11- -6 -5 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-1083,13900] |
[a1,a2,a3,a4,a6] |
Generators |
[-35:94:1] [-8:148:1] |
Generators of the group modulo torsion |
j |
-192699928576/2982771 |
j-invariant |
L |
2.9987100577143 |
L(r)(E,1)/r! |
Ω |
1.4672173464298 |
Real period |
R |
0.17031730535191 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2739b1 90387p1 |
Quadratic twists by: -3 -11 |