Atkin-Lehner |
23- 41- |
Signs for the Atkin-Lehner involutions |
Class |
21689a |
Isogeny class |
Conductor |
21689 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
Δ |
3210750396521 = 238 · 41 |
Discriminant |
Eigenvalues |
1 0 2 -2 -2 6 -8 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-115421,-15063928] |
[a1,a2,a3,a4,a6] |
Generators |
[17803042842362414:262946583594855623:34575881164552] |
Generators of the group modulo torsion |
j |
1148717693817/21689 |
j-invariant |
L |
5.8656853040136 |
L(r)(E,1)/r! |
Ω |
0.25901723449057 |
Real period |
R |
22.645926691134 |
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 |
943a2 |
Quadratic twists by: -23 |