Atkin-Lehner |
2- 3+ 13- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
33072o |
Isogeny class |
Conductor |
33072 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
25920 |
Modular degree for the optimal curve |
Δ |
-12877443072 = -1 · 212 · 33 · 133 · 53 |
Discriminant |
Eigenvalues |
2- 3+ 0 4 -3 13- 6 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-213,5661] |
[a1,a2,a3,a4,a6] |
Generators |
[-20:39:1] |
Generators of the group modulo torsion |
j |
-262144000/3143907 |
j-invariant |
L |
5.858545857071 |
L(r)(E,1)/r! |
Ω |
1.0722197928762 |
Real period |
R |
1.8213137194427 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2067b1 99216bq1 |
Quadratic twists by: -4 -3 |