Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 14 x + 122 x^{2} - 675 x^{3} + 2806 x^{4} - 7406 x^{5} + 12167 x^{6}$ |
| Frobenius angles: | $\pm0.218403948752$, $\pm0.290498332792$, $\pm0.476349481559$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.20045493099.1 |
| Galois group: | $S_4\times C_2$ |
| Cyclic group of points: | yes |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $7001$ | $162360191$ | $1854596075453$ | $21984113605679659$ | $266791743307481792251$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $10$ | $578$ | $12523$ | $280730$ | $6440120$ | $148054673$ | $3404756834$ | $78309835346$ | $1801149273580$ | $41426522216678$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains no Jacobian of a hyperelliptic curve, but it is unknown whether it contains a Jacobian of a non-hyperelliptic curve.
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 6.0.20045493099.1. |
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.o_es_zz | $2$ | (not in LMFDB) |