Atkin-Lehner |
2+ 3- 11- 43- |
Signs for the Atkin-Lehner involutions |
Class |
68112p |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
57344 |
Modular degree for the optimal curve |
Δ |
36197509392 = 24 · 314 · 11 · 43 |
Discriminant |
Eigenvalues |
2+ 3- 0 -1 11- 6 -6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5835,171313] |
[a1,a2,a3,a4,a6] |
j |
1883643808000/3103353 |
j-invariant |
L |
2.3153885787986 |
L(r)(E,1)/r! |
Ω |
1.1576942965602 |
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 |
34056b1 22704j1 |
Quadratic twists by: -4 -3 |