Atkin-Lehner |
2- 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
89232bv |
Isogeny class |
Conductor |
89232 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
435456 |
Modular degree for the optimal curve |
Δ |
2913729290993664 = 215 · 33 · 117 · 132 |
Discriminant |
Eigenvalues |
2- 3- 1 -2 11+ 13+ 5 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-69840,-6635628] |
[a1,a2,a3,a4,a6] |
Generators |
[-174:528:1] |
Generators of the group modulo torsion |
j |
54424690756969/4209228936 |
j-invariant |
L |
8.9863126012204 |
L(r)(E,1)/r! |
Ω |
0.29511746725455 |
Real period |
R |
2.5374959709375 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999909641 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11154z1 89232cl1 |
Quadratic twists by: -4 13 |