Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + 2 x + x^{2} + 2 x^{4} + 8 x^{5} + 8 x^{6}$ |
| Frobenius angles: | $\pm0.229446223460$, $\pm0.660092868705$, $\pm0.930646645245$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 6.0.2580992.1 |
| Galois group: | $D_{6}$ |
| Jacobians: | $0$ |
| Cyclic group of points: | yes |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1/2, 1/2, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $22$ | $44$ | $550$ | $5984$ | $65362$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $5$ | $3$ | $11$ | $23$ | $55$ | $51$ | $131$ | $255$ | $407$ | $1043$ |
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 $\F_{2}$.
Endomorphism algebra over $\F_{2}$| The endomorphism algebra of this simple isogeny class is 6.0.2580992.1. |
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 |
|---|---|---|
| 3.2.ac_b_a | $2$ | 3.4.ac_f_am |