Atkin-Lehner |
2- 3+ 7- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
19992u |
Isogeny class |
Conductor |
19992 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
Δ |
1024209411176448 = 211 · 36 · 79 · 17 |
Discriminant |
Eigenvalues |
2- 3+ 2 7- 0 -2 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-8887003792,-322460981936372] |
[a1,a2,a3,a4,a6] |
Generators |
[643991765129892891835748954612951640024229640608537234016906671225295152461959902829902336945140093:269110044290529107945838297053592278571307732672990423536759138419433715496652539114494391019056565800:2909344220071098089009484446843668690081035076165099659833559299706111700706233424466559189241] |
Generators of the group modulo torsion |
j |
322159999717985454060440834/4250799 |
j-invariant |
L |
4.8513672770804 |
L(r)(E,1)/r! |
Ω |
0.015549295367583 |
Real period |
R |
155.99958591032 |
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 |
39984o4 59976s4 2856h4 |
Quadratic twists by: -4 -3 -7 |