Atkin-Lehner |
2- 5- 29+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
68150x |
Isogeny class |
Conductor |
68150 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
169344 |
Modular degree for the optimal curve |
Δ |
2099150848000 = 218 · 53 · 29 · 472 |
Discriminant |
Eigenvalues |
2- 0 5- 4 -2 -4 -2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-40110,3101117] |
[a1,a2,a3,a4,a6] |
Generators |
[89:435:1] |
Generators of the group modulo torsion |
j |
57090196019543877/16793206784 |
j-invariant |
L |
10.566786028833 |
L(r)(E,1)/r! |
Ω |
0.80748141925205 |
Real period |
R |
0.72700579143907 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998778 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68150h1 |
Quadratic twists by: 5 |