Atkin-Lehner |
2- 3+ 11- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
78144ca |
Isogeny class |
Conductor |
78144 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
-15363735552 = -1 · 222 · 32 · 11 · 37 |
Discriminant |
Eigenvalues |
2- 3+ 0 -2 11- -2 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,287,-5759] |
[a1,a2,a3,a4,a6] |
Generators |
[40:261:1] |
Generators of the group modulo torsion |
j |
9938375/58608 |
j-invariant |
L |
4.245899440357 |
L(r)(E,1)/r! |
Ω |
0.62255793383226 |
Real period |
R |
3.4100436346602 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003329 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
78144u1 19536bb1 |
Quadratic twists by: -4 8 |