Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + 36 x^{2} + 9 x^{3} + 828 x^{4} + 12167 x^{6}$ |
| Frobenius angles: | $\pm0.301426342572$, $\pm0.490927478111$, $\pm0.709897458148$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.32990740011.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $13041$ | $169832943$ | $1805076183393$ | $21970940867207451$ | $266568253521193816731$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $24$ | $602$ | $12195$ | $280562$ | $6434724$ | $148023113$ | $3404854932$ | $78309987650$ | $1801152727884$ | $41426548682162$ |
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 6.0.32990740011.1. |
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.a_bk_aj | $2$ | (not in LMFDB) |