Atkin-Lehner |
2- 11+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
8228b |
Isogeny class |
Conductor |
8228 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
2448 |
Modular degree for the optimal curve |
Δ |
-5792512 = -1 · 28 · 113 · 17 |
Discriminant |
Eigenvalues |
2- -2 0 1 11+ 2 17- -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1173,15079] |
[a1,a2,a3,a4,a6] |
Generators |
[18:11:1] |
Generators of the group modulo torsion |
j |
-524288000/17 |
j-invariant |
L |
3.0038412530434 |
L(r)(E,1)/r! |
Ω |
2.2387759491581 |
Real period |
R |
0.67086687575257 |
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 |
32912r1 74052c1 8228a1 |
Quadratic twists by: -4 -3 -11 |