Atkin-Lehner |
2+ 3+ 5- 47- |
Signs for the Atkin-Lehner involutions |
Class |
45120r |
Isogeny class |
Conductor |
45120 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
-4620288000 = -1 · 218 · 3 · 53 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -3 2 1 3 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,415,225] |
[a1,a2,a3,a4,a6] |
Generators |
[25:160:1] |
Generators of the group modulo torsion |
j |
30080231/17625 |
j-invariant |
L |
4.8854062751159 |
L(r)(E,1)/r! |
Ω |
0.83308943917443 |
Real period |
R |
0.48868365201756 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999992 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
45120cw1 705d1 |
Quadratic twists by: -4 8 |