Atkin-Lehner |
2+ 3- 5- 13- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
54990r |
Isogeny class |
Conductor |
54990 |
Conductor |
∏ cp |
160 |
Product of Tamagawa factors cp |
deg |
691200 |
Modular degree for the optimal curve |
Δ |
-123654069213480000 = -1 · 26 · 311 · 54 · 135 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 5- -3 -5 13- -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-90144,19891008] |
[a1,a2,a3,a4,a6] |
Generators |
[24:4200:1] [-288:4824:1] |
Generators of the group modulo torsion |
j |
-111124384814596609/169621494120000 |
j-invariant |
L |
7.0039704053333 |
L(r)(E,1)/r! |
Ω |
0.29685721156742 |
Real period |
R |
0.14746084422944 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
18330bd1 |
Quadratic twists by: -3 |