Atkin-Lehner |
2+ 3- 23+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
51336f |
Isogeny class |
Conductor |
51336 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
22272 |
Modular degree for the optimal curve |
Δ |
-191277936 = -1 · 24 · 36 · 232 · 31 |
Discriminant |
Eigenvalues |
2+ 3- -3 -5 2 0 -4 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-399,3139] |
[a1,a2,a3,a4,a6] |
Generators |
[11:-9:1] [15:23:1] |
Generators of the group modulo torsion |
j |
-602275072/16399 |
j-invariant |
L |
7.0954017653992 |
L(r)(E,1)/r! |
Ω |
1.7875380073236 |
Real period |
R |
0.4961713916243 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999979 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
102672s1 5704b1 |
Quadratic twists by: -4 -3 |