Atkin-Lehner |
3- 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
33033q |
Isogeny class |
Conductor |
33033 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
63360 |
Modular degree for the optimal curve |
Δ |
-13518114112503 = -1 · 32 · 72 · 119 · 13 |
Discriminant |
Eigenvalues |
1 3- -2 7+ 11+ 13- 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-8957,370379] |
[a1,a2,a3,a4,a6] |
Generators |
[-63:859:1] |
Generators of the group modulo torsion |
j |
-33698267/5733 |
j-invariant |
L |
5.9818498329384 |
L(r)(E,1)/r! |
Ω |
0.68051190451912 |
Real period |
R |
4.3951103523791 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
99099m1 33033x1 |
Quadratic twists by: -3 -11 |