# Properties

 Label 3.23.ax_jh_aces Base Field $\F_{23}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $( 1 - 8 x + 23 x^{2} )( 1 - 15 x + 98 x^{2} - 345 x^{3} + 529 x^{4} )$ Frobenius angles: $\pm0.0252283536038$, $\pm0.186011988595$, $\pm0.308104979730$ Angle rank: $2$ (numerical)

This isogeny class is not simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $3$ Slopes: $[0, 0, 0, 1, 1, 1]$

## Point counts

This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4288 135569408 1806958037248 21955079523926016 266619757351864728128 3243700904414625914814464 39470030019402046689305152448 480247748814072984699441493573632 5843206516583315293893099586494221056 71094334669235078925275532301062062317568

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 483 12208 280359 6435971 148015356 3404691389 78310493615 1801151265424 41426502984843

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.ai $\times$ 2.23.ap_du and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
Endomorphism algebra over $\overline{\F}_{23}$
 The base change of $A$ to $\F_{23^{6}}$ is 1.148035889.abgac 2 $\times$ 1.148035889.bhqk. The endomorphism algebra for each factor is: 1.148035889.abgac 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-51})$$$)$ 1.148035889.bhqk : $$\Q(\sqrt{-7})$$.
All geometric endomorphisms are defined over $\F_{23^{6}}$.
Remainder of endomorphism lattice by field
• Endomorphism algebra over $\F_{23^{2}}$  The base change of $A$ to $\F_{23^{2}}$ is 1.529.as $\times$ 2.529.abd_ma. The endomorphism algebra for each factor is:
• Endomorphism algebra over $\F_{23^{3}}$  The base change of $A$ to $\F_{23^{3}}$ is 1.12167.bo $\times$ 2.12167.a_abgac. The endomorphism algebra for each factor is:

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 3.23.ah_b_dq $2$ (not in LMFDB) 3.23.h_b_adq $2$ (not in LMFDB) 3.23.x_jh_ces $2$ (not in LMFDB) 3.23.ai_ca_aiy $3$ (not in LMFDB) 3.23.h_b_adq $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.23.ah_b_dq $2$ (not in LMFDB) 3.23.h_b_adq $2$ (not in LMFDB) 3.23.x_jh_ces $2$ (not in LMFDB) 3.23.ai_ca_aiy $3$ (not in LMFDB) 3.23.h_b_adq $3$ (not in LMFDB) 3.23.ai_ca_aiy $6$ (not in LMFDB) 3.23.ah_b_dq $6$ (not in LMFDB) 3.23.i_ca_iy $6$ (not in LMFDB) 3.23.ai_ag_iy $12$ (not in LMFDB) 3.23.i_ag_aiy $12$ (not in LMFDB)