Atkin-Lehner |
2+ 3- 5+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
48960cg |
Isogeny class |
Conductor |
48960 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
349440 |
Modular degree for the optimal curve |
Δ |
-4239670284288000 = -1 · 215 · 36 · 53 · 175 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -2 -4 1 17- 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-195948,33532272] |
[a1,a2,a3,a4,a6] |
Generators |
[334:2312:1] |
Generators of the group modulo torsion |
j |
-34831225434312/177482125 |
j-invariant |
L |
4.7316227866824 |
L(r)(E,1)/r! |
Ω |
0.44013823510447 |
Real period |
R |
0.53751553594896 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000013 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48960cf1 24480bj1 5440g1 |
Quadratic twists by: -4 8 -3 |