Invariants
| Base field: | $\F_{2^{3}}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 8 x + 23 x^{2} - 47 x^{3} + 184 x^{4} - 512 x^{5} + 512 x^{6}$ |
| Frobenius angles: | $\pm0.0601780301132$, $\pm0.124308289561$, $\pm0.663981835019$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.28413583.1 |
| Galois group: | $S_4\times C_2$ |
| Isomorphism classes: | 3 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $153$ | $196911$ | $110033775$ | $68176298619$ | $35311796037243$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $1$ | $47$ | $412$ | $4063$ | $32886$ | $261404$ | $2100400$ | $16789495$ | $134219221$ | $1073837632$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{2^{3}}$.
Endomorphism algebra over $\F_{2^{3}}$| The endomorphism algebra of this simple isogeny class is 6.0.28413583.1. |
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 |
|---|---|---|
| 3.8.i_x_bv | $2$ | (not in LMFDB) |