# Properties

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

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $( 1 - 7 x + 23 x^{2} )( 1 - 15 x + 98 x^{2} - 345 x^{3} + 529 x^{4} )$ Frobenius angles: $\pm0.0252283536038$, $\pm0.239612957690$, $\pm0.308104979730$ 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 $A(\F_{q^r})$ 4556 139541168 1821759462848 21979728282373056 266585443173655141756 3243306556454999711166464 39468526900289286522868864564 480244304486641330202298302967552 5843203369432517605014798526304526656 71094347580176791451799651413789902718768

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 2 498 12308 280674 6435142 147997356 3404561722 78309931970 1801150295324 41426510508018

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.ah $\times$ 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.hac. The endomorphism algebra for each factor is: 1.148035889.abgac 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-51})$$$)$ 1.148035889.hac : $$\Q(\sqrt{-43})$$.
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.ad $\times$ 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.fk $\times$ 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.ai_q_ae $2$ (not in LMFDB) 3.23.i_q_e $2$ (not in LMFDB) 3.23.w_is_cay $2$ (not in LMFDB) 3.23.ah_ca_ahv $3$ (not in LMFDB) 3.23.i_q_e $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.23.ai_q_ae $2$ (not in LMFDB) 3.23.i_q_e $2$ (not in LMFDB) 3.23.w_is_cay $2$ (not in LMFDB) 3.23.ah_ca_ahv $3$ (not in LMFDB) 3.23.i_q_e $3$ (not in LMFDB) 3.23.h_ca_hv $6$ (not in LMFDB) 3.23.ah_ag_hv $12$ (not in LMFDB) 3.23.h_ag_ahv $12$ (not in LMFDB)