Atkin-Lehner |
2+ 7+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
13664a |
Isogeny class |
Conductor |
13664 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1664 |
Modular degree for the optimal curve |
Δ |
1748992 = 212 · 7 · 61 |
Discriminant |
Eigenvalues |
2+ 1 0 7+ 5 -2 -3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-33,-49] |
[a1,a2,a3,a4,a6] |
Generators |
[-5:4:1] |
Generators of the group modulo torsion |
j |
1000000/427 |
j-invariant |
L |
5.4738064323725 |
L(r)(E,1)/r! |
Ω |
2.0648371538813 |
Real period |
R |
0.66274069387061 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
13664e1 27328u1 122976x1 95648j1 |
Quadratic twists by: -4 8 -3 -7 |