Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 8 x + 23 x^{2} )( 1 - 16 x + 108 x^{2} - 368 x^{3} + 529 x^{4} )$ |
| $1 - 24 x + 259 x^{2} - 1600 x^{3} + 5957 x^{4} - 12696 x^{5} + 12167 x^{6}$ | |
| Frobenius angles: | $\pm0.0613235619868$, $\pm0.186011988595$, $\pm0.259095524151$ |
| Angle rank: | $3$ (numerical) |
This isogeny class is not 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4064$ | $132909056$ | $1804761744800$ | $21995043121823744$ | $266846417175622796384$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $0$ | $472$ | $12192$ | $280868$ | $6441440$ | $148044664$ | $3404770432$ | $78310444540$ | $1801150348416$ | $41426507675832$ |
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 isogeny class factors as 1.23.ai $\times$ 2.23.aq_ee and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.ai_d_ey | $2$ | (not in LMFDB) |
| 3.23.i_d_aey | $2$ | (not in LMFDB) |
| 3.23.y_jz_cjo | $2$ | (not in LMFDB) |