Invariants
| Base field: | $\F_{2^{2}}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 7 x + 26 x^{2} - 63 x^{3} + 104 x^{4} - 112 x^{5} + 64 x^{6}$ |
| Frobenius angles: | $\pm0.100587617290$, $\pm0.290662784222$, $\pm0.439716826337$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.573839.1 |
| Galois group: | $A_4\times C_2$ |
| Isomorphism classes: | 1 |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $3$ |
| Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $13$ | $4901$ | $326677$ | $16472261$ | $1032240313$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $20$ | $79$ | $252$ | $983$ | $4103$ | $16532$ | $65660$ | $262474$ | $1051935$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{2^{2}}$.
Endomorphism algebra over $\F_{2^{2}}$| The endomorphism algebra of this simple isogeny class is 6.0.573839.1. |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
| Twist | Extension degree | Common base change |
|---|---|---|
| 3.4.h_ba_cl | $2$ | 3.16.d_c_ab |