Atkin-Lehner |
2+ 3- 7+ 13- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
33306g |
Isogeny class |
Conductor |
33306 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
53254080 |
Modular degree for the optimal curve |
Δ |
-2.1432925808551E+27 |
Discriminant |
Eigenvalues |
2+ 3- -3 7+ 2 13- -1 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-10688161450,425312031019292] |
[a1,a2,a3,a4,a6] |
Generators |
[1721844966:-24681809408:29791] |
Generators of the group modulo torsion |
j |
-135030765064687393171032461411563033/2143292580855121726905778176 |
j-invariant |
L |
4.1190370188149 |
L(r)(E,1)/r! |
Ω |
0.042439276961884 |
Real period |
R |
8.0880992673255 |
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 |
99918y1 |
Quadratic twists by: -3 |