Atkin-Lehner |
2- 3+ 5+ 7+ |
Signs for the Atkin-Lehner involutions |
Class |
47040dw |
Isogeny class |
Conductor |
47040 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
129024 |
Modular degree for the optimal curve |
Δ |
-177094686720000 = -1 · 214 · 3 · 54 · 78 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7+ -2 -1 -4 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,3659,-635795] |
[a1,a2,a3,a4,a6] |
j |
57344/1875 |
j-invariant |
L |
0.54977223874872 |
L(r)(E,1)/r! |
Ω |
0.27488611933698 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47040by1 11760cl1 47040gy1 |
Quadratic twists by: -4 8 -7 |