Atkin-Lehner |
2+ 3+ 13+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
55224a |
Isogeny class |
Conductor |
55224 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
18454535424 = 28 · 33 · 13 · 593 |
Discriminant |
Eigenvalues |
2+ 3+ 1 2 2 13+ 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3132,-67148] |
[a1,a2,a3,a4,a6] |
Generators |
[-34:6:1] |
Generators of the group modulo torsion |
j |
491569855488/2669927 |
j-invariant |
L |
7.7776748617301 |
L(r)(E,1)/r! |
Ω |
0.63839008880963 |
Real period |
R |
1.5229079754695 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000076 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
110448c1 55224k1 |
Quadratic twists by: -4 -3 |