Atkin-Lehner |
2- 3- 5- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
47190cz |
Isogeny class |
Conductor |
47190 |
Conductor |
∏ cp |
288 |
Product of Tamagawa factors cp |
deg |
829440 |
Modular degree for the optimal curve |
Δ |
-3178888615509750000 = -1 · 24 · 33 · 56 · 118 · 133 |
Discriminant |
Eigenvalues |
2- 3- 5- -2 11- 13+ -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-72300,86101632] |
[a1,a2,a3,a4,a6] |
Generators |
[54:-9102:1] |
Generators of the group modulo torsion |
j |
-23592983745241/1794399750000 |
j-invariant |
L |
11.227718747181 |
L(r)(E,1)/r! |
Ω |
0.20791421664567 |
Real period |
R |
0.7500234503961 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000019 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4290o1 |
Quadratic twists by: -11 |