Atkin-Lehner |
2- 13+ 79- |
Signs for the Atkin-Lehner involutions |
Class |
8216d |
Isogeny class |
Conductor |
8216 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
9600 |
Modular degree for the optimal curve |
Δ |
-390469540864 = -1 · 210 · 136 · 79 |
Discriminant |
Eigenvalues |
2- -2 2 -2 4 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-5832,-176000] |
[a1,a2,a3,a4,a6] |
Generators |
[10947000:117974000:68921] |
Generators of the group modulo torsion |
j |
-21426476889892/381317911 |
j-invariant |
L |
3.1932420954801 |
L(r)(E,1)/r! |
Ω |
0.27286659709005 |
Real period |
R |
11.702576018956 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
16432a1 65728l1 73944k1 106808f1 |
Quadratic twists by: -4 8 -3 13 |