Atkin-Lehner |
3- 7- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
33033ba |
Isogeny class |
Conductor |
33033 |
Conductor |
∏ cp |
90 |
Product of Tamagawa factors cp |
deg |
103680 |
Modular degree for the optimal curve |
Δ |
248527416958821 = 315 · 7 · 114 · 132 |
Discriminant |
Eigenvalues |
0 3- 3 7- 11- 13- -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-19279,690949] |
[a1,a2,a3,a4,a6] |
Generators |
[-109:1228:1] |
Generators of the group modulo torsion |
j |
54128875896832/16974756981 |
j-invariant |
L |
7.2154762056169 |
L(r)(E,1)/r! |
Ω |
0.51306117725458 |
Real period |
R |
1.4063578624731 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999998 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
99099bz1 33033s1 |
Quadratic twists by: -3 -11 |