Atkin-Lehner |
17+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
47753b |
Isogeny class |
Conductor |
47753 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
4155840 |
Modular degree for the optimal curve |
Δ |
8.8399857248404E+19 |
Discriminant |
Eigenvalues |
1 -2 0 -4 0 2 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-83140841,291782267895] |
[a1,a2,a3,a4,a6] |
Generators |
[112612241144742:-84605420764055:21438614952] |
Generators of the group modulo torsion |
j |
2867554803676902625/3988378313 |
j-invariant |
L |
2.5923687264159 |
L(r)(E,1)/r! |
Ω |
0.16227606758503 |
Real period |
R |
15.975052667968 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999783 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
901b1 |
Quadratic twists by: 53 |