Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + 6 x + 54 x^{2} + 177 x^{3} + 1242 x^{4} + 3174 x^{5} + 12167 x^{6}$ |
| Frobenius angles: | $\pm0.363523276948$, $\pm0.661492925590$, $\pm0.687443643606$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.35060627619.1 |
| Galois group: | $S_4\times C_2$ |
| Cyclic group of points: | no |
| Non-cyclic primes: | $3$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $16821$ | $170009847$ | $1767748309929$ | $22022139336152571$ | $266619363945839534511$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $30$ | $602$ | $11943$ | $281210$ | $6435960$ | $147968681$ | $3404985222$ | $78311862962$ | $1801149536052$ | $41426522339342$ |
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 6.0.35060627619.1. |
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.ag_cc_agv | $2$ | (not in LMFDB) |