Atkin-Lehner |
2- 3- 11- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
78144cx |
Isogeny class |
Conductor |
78144 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
172032 |
Modular degree for the optimal curve |
Δ |
539591196672 = 214 · 37 · 11 · 372 |
Discriminant |
Eigenvalues |
2- 3- 0 4 11- 0 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-32273,-2242065] |
[a1,a2,a3,a4,a6] |
j |
226900390642000/32934033 |
j-invariant |
L |
4.986782351302 |
L(r)(E,1)/r! |
Ω |
0.35619874201603 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
78144c1 19536a1 |
Quadratic twists by: -4 8 |