Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 22 x + 225 x^{2} - 1366 x^{3} + 5175 x^{4} - 11638 x^{5} + 12167 x^{6}$ |
| Frobenius angles: | $\pm0.0404981459123$, $\pm0.210373719318$, $\pm0.328791241931$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.1108246464.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4542$ | $138957948$ | $1816458854922$ | $21960510012207216$ | $266581691987972792142$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $2$ | $496$ | $12272$ | $280428$ | $6435052$ | $148010596$ | $3404693938$ | $78310609820$ | $1801151680046$ | $41426503189036$ |
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 6.0.1108246464.1. |
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_ir_cao | $2$ | (not in LMFDB) |