Atkin-Lehner |
2+ 11- 47- |
Signs for the Atkin-Lehner involutions |
Class |
33088q |
Isogeny class |
Conductor |
33088 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-398114816 = -1 · 214 · 11 · 472 |
Discriminant |
Eigenvalues |
2+ -1 -3 0 11- 6 -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-197,1501] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:47:1] |
Generators of the group modulo torsion |
j |
-51868672/24299 |
j-invariant |
L |
3.2301218882575 |
L(r)(E,1)/r! |
Ω |
1.5745605234559 |
Real period |
R |
1.0257217300126 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33088y1 4136d1 |
Quadratic twists by: -4 8 |