Atkin-Lehner |
3- 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
33033q |
Isogeny class |
Conductor |
33033 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
Δ |
8368356355359 = 3 · 7 · 119 · 132 |
Discriminant |
Eigenvalues |
1 3- -2 7+ 11+ 13- 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-148712,22060355] |
[a1,a2,a3,a4,a6] |
Generators |
[33236:573231:64] |
Generators of the group modulo torsion |
j |
154249367147/3549 |
j-invariant |
L |
5.9818498329384 |
L(r)(E,1)/r! |
Ω |
0.68051190451912 |
Real period |
R |
8.7902207047583 |
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 |
99099m2 33033x2 |
Quadratic twists by: -3 -11 |