Atkin-Lehner |
2- 3+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
89232bg |
Isogeny class |
Conductor |
89232 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-31045814452224 = -1 · 217 · 34 · 113 · 133 |
Discriminant |
Eigenvalues |
2- 3+ -1 1 11+ 13- -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-8896,-416768] |
[a1,a2,a3,a4,a6] |
Generators |
[256:-3744:1] |
Generators of the group modulo torsion |
j |
-8653002877/3449952 |
j-invariant |
L |
4.292388241164 |
L(r)(E,1)/r! |
Ω |
0.24104969043499 |
Real period |
R |
1.1129417539777 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999992703 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11154bj1 89232bt1 |
Quadratic twists by: -4 13 |