Atkin-Lehner |
2+ 7- 41- |
Signs for the Atkin-Lehner involutions |
Class |
128576bp |
Isogeny class |
Conductor |
128576 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2064384 |
Modular degree for the optimal curve |
Δ |
1015144902280871936 = 232 · 78 · 41 |
Discriminant |
Eigenvalues |
2+ 2 2 7- 2 4 -6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-265057,-20132895] |
[a1,a2,a3,a4,a6] |
Generators |
[-12292193019503821380:-53219702662836402455:26680508532923328] |
Generators of the group modulo torsion |
j |
66775173193/32915456 |
j-invariant |
L |
13.15074742549 |
L(r)(E,1)/r! |
Ω |
0.221279554497 |
Real period |
R |
29.715233946242 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999746726 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
128576cz1 4018i1 18368i1 |
Quadratic twists by: -4 8 -7 |