Atkin-Lehner |
2+ 3- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
51984l |
Isogeny class |
Conductor |
51984 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
875520 |
Modular degree for the optimal curve |
Δ |
-770198333958150912 = -1 · 28 · 311 · 198 |
Discriminant |
Eigenvalues |
2+ 3- 2 5 -4 5 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-144039,-47176202] |
[a1,a2,a3,a4,a6] |
j |
-104272/243 |
j-invariant |
L |
4.120380836935 |
L(r)(E,1)/r! |
Ω |
0.11445502325547 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25992w1 17328j1 51984w1 |
Quadratic twists by: -4 -3 -19 |