Atkin-Lehner |
2+ 3+ 7- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
42042q |
Isogeny class |
Conductor |
42042 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
497664 |
Modular degree for the optimal curve |
Δ |
32774002424235072 = 26 · 33 · 77 · 116 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7- 11- 13+ -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-176425,-27233723] |
[a1,a2,a3,a4,a6] |
Generators |
[-211:914:1] |
Generators of the group modulo torsion |
j |
5162020164015625/278574424128 |
j-invariant |
L |
3.0045979970166 |
L(r)(E,1)/r! |
Ω |
0.23373088345899 |
Real period |
R |
1.0712455397958 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
126126eq1 6006q1 |
Quadratic twists by: -3 -7 |