Atkin-Lehner |
3+ 11- 67- |
Signs for the Atkin-Lehner involutions |
Class |
6633b |
Isogeny class |
Conductor |
6633 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
21312 |
Modular degree for the optimal curve |
Δ |
716310093609 = 39 · 112 · 673 |
Discriminant |
Eigenvalues |
1 3+ -2 -2 11- 4 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-169278,26849375] |
[a1,a2,a3,a4,a6] |
Generators |
[-194:7333:1] |
Generators of the group modulo torsion |
j |
27254324376836019/36392323 |
j-invariant |
L |
3.9576707325423 |
L(r)(E,1)/r! |
Ω |
0.76546509799847 |
Real period |
R |
1.7234274703884 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
106128s1 6633a1 72963c1 |
Quadratic twists by: -4 -3 -11 |