Atkin-Lehner |
17+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
47753a |
Isogeny class |
Conductor |
47753 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
471744 |
Modular degree for the optimal curve |
Δ |
305881858991016593 = 173 · 538 |
Discriminant |
Eigenvalues |
1 0 0 2 -6 6 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-237887,-35805928] |
[a1,a2,a3,a4,a6] |
Generators |
[-76757463412950524:-177666163585682982:206309829721969] |
Generators of the group modulo torsion |
j |
67170974625/13800617 |
j-invariant |
L |
6.1515655375457 |
L(r)(E,1)/r! |
Ω |
0.21929842507236 |
Real period |
R |
28.051115896122 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000006 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
901a1 |
Quadratic twists by: 53 |