Atkin-Lehner |
2- 7+ 17+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
27608d |
Isogeny class |
Conductor |
27608 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
8960 |
Modular degree for the optimal curve |
Δ |
-420525056 = -1 · 210 · 72 · 172 · 29 |
Discriminant |
Eigenvalues |
2- -1 1 7+ -5 1 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-320,2524] |
[a1,a2,a3,a4,a6] |
Generators |
[-10:68:1] [6:-28:1] |
Generators of the group modulo torsion |
j |
-3550014724/410669 |
j-invariant |
L |
6.9116096021832 |
L(r)(E,1)/r! |
Ω |
1.6318820068012 |
Real period |
R |
0.52942013985825 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
55216d1 |
Quadratic twists by: -4 |