Atkin-Lehner |
2- 3+ 19+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
81168bp |
Isogeny class |
Conductor |
81168 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
506880 |
Modular degree for the optimal curve |
Δ |
7059431586004992 = 234 · 35 · 19 · 89 |
Discriminant |
Eigenvalues |
2- 3+ 0 2 4 6 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-126048,-16701696] |
[a1,a2,a3,a4,a6] |
Generators |
[8552783503721360:-149218571840956781:14872416882688] |
Generators of the group modulo torsion |
j |
54072330385398625/1723494039552 |
j-invariant |
L |
6.8234782692001 |
L(r)(E,1)/r! |
Ω |
0.25387101600854 |
Real period |
R |
26.877736479915 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001516 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10146q1 |
Quadratic twists by: -4 |