Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - x + 16 x^{2} - 33 x^{3} + 368 x^{4} - 529 x^{5} + 12167 x^{6}$ |
| Frobenius angles: | $\pm0.204444419764$, $\pm0.491887401265$, $\pm0.756757602248$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.2928367664.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $11989$ | $157235735$ | $1793746991296$ | $21984323888114675$ | $266654655561132160159$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $23$ | $561$ | $12116$ | $280733$ | $6436813$ | $148081452$ | $3404940611$ | $78309654357$ | $1801151922908$ | $41426508210761$ |
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 6.0.2928367664.1. |
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.b_q_bh | $2$ | (not in LMFDB) |