Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 22 x + 226 x^{2} - 1375 x^{3} + 5198 x^{4} - 11638 x^{5} + 12167 x^{6}$ |
| Frobenius angles: | $\pm0.0527001661086$, $\pm0.227767494529$, $\pm0.313634986415$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.651528243.1 |
| Galois group: | $S_4\times C_2$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4557$ | $139567239$ | $1822286102553$ | $21986705596018779$ | $266638895595308819247$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $2$ | $498$ | $12311$ | $280762$ | $6436432$ | $148009833$ | $3404649250$ | $78310390226$ | $1801152072260$ | $41426515736358$ |
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 $\F_{23}$.
Endomorphism algebra over $\F_{23}$| The endomorphism algebra of this simple isogeny class is 6.0.651528243.1. |
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 |
|---|---|---|
| 3.23.w_is_cax | $2$ | (not in LMFDB) |