Atkin-Lehner |
2+ 3+ 13- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
51168d |
Isogeny class |
Conductor |
51168 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
22272 |
Modular degree for the optimal curve |
Δ |
-85143552 = -1 · 212 · 3 · 132 · 41 |
Discriminant |
Eigenvalues |
2+ 3+ 4 4 -3 13- 7 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,99,-267] |
[a1,a2,a3,a4,a6] |
j |
25934336/20787 |
j-invariant |
L |
4.2581488181922 |
L(r)(E,1)/r! |
Ω |
1.0645372045477 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51168r1 102336z1 |
Quadratic twists by: -4 8 |