Atkin-Lehner |
3- 7- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
21021m |
Isogeny class |
Conductor |
21021 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
32256 |
Modular degree for the optimal curve |
Δ |
-7385749371 = -1 · 34 · 73 · 112 · 133 |
Discriminant |
Eigenvalues |
-2 3- -3 7- 11+ 13- -2 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-1892,31322] |
[a1,a2,a3,a4,a6] |
Generators |
[-47:136:1] [-8:214:1] |
Generators of the group modulo torsion |
j |
-2184854450176/21532797 |
j-invariant |
L |
4.1447843655483 |
L(r)(E,1)/r! |
Ω |
1.3280791897349 |
Real period |
R |
0.06501846798718 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000005 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
63063bg1 21021d1 |
Quadratic twists by: -3 -7 |