Atkin-Lehner |
2+ 3+ 13+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
11856c |
Isogeny class |
Conductor |
11856 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
277440 |
Modular degree for the optimal curve |
Δ |
-8513392169029183488 = -1 · 211 · 317 · 13 · 195 |
Discriminant |
Eigenvalues |
2+ 3+ 0 5 -1 13+ 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-319608,156770640] |
[a1,a2,a3,a4,a6] |
j |
-1762982669155531250/4156929770033781 |
j-invariant |
L |
2.0581403058065 |
L(r)(E,1)/r! |
Ω |
0.20581403058065 |
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 |
5928f1 47424dl1 35568m1 |
Quadratic twists by: -4 8 -3 |