Atkin-Lehner |
2- 5- 13+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
89570ba |
Isogeny class |
Conductor |
89570 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
6082560 |
Modular degree for the optimal curve |
Δ |
-180928098091520000 = -1 · 212 · 54 · 132 · 535 |
Discriminant |
Eigenvalues |
2- 3 5- -4 2 13+ -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-7838187,-8444462789] |
[a1,a2,a3,a4,a6] |
Generators |
[101757:3314378:27] |
Generators of the group modulo torsion |
j |
-315125695344049881290649/1070580462080000 |
j-invariant |
L |
18.247005970372 |
L(r)(E,1)/r! |
Ω |
0.04511443987598 |
Real period |
R |
8.4262590582037 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001455 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
89570b1 |
Quadratic twists by: 13 |