# Properties

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

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $( 1 - 9 x + 23 x^{2} )( 1 - 15 x + 98 x^{2} - 345 x^{3} + 529 x^{4} )$ Frobenius angles: $\pm0.0252283536038$, $\pm0.112386341891$, $\pm0.308104979730$ 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 $A(\F_{q^r})$ 4020 131068080 1785051927360 21884576249764800 266455388712937988100 3243480420088754908508160 39470302330561230206080853580 480250881741851255738962989100800 5843219747645175641319202733299515840 71094375101771983017935112122225134340400

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 0 466 12060 279458 6432000 148005292 3404714880 78311004482 1801155343860 41426526544786

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.aj $\times$ 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.sti. The endomorphism algebra for each factor is: 1.148035889.abgac 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-51})$$$)$ 1.148035889.sti : $$\Q(\sqrt{-11})$$.
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.abj $\times$ 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.aee $\times$ 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.ag_ao_hk $2$ (not in LMFDB) 3.23.g_ao_ahk $2$ (not in LMFDB) 3.23.y_jw_cim $2$ (not in LMFDB) 3.23.aj_ca_akb $3$ (not in LMFDB) 3.23.g_ao_ahk $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.23.ag_ao_hk $2$ (not in LMFDB) 3.23.g_ao_ahk $2$ (not in LMFDB) 3.23.y_jw_cim $2$ (not in LMFDB) 3.23.aj_ca_akb $3$ (not in LMFDB) 3.23.g_ao_ahk $3$ (not in LMFDB) 3.23.j_ca_kb $6$ (not in LMFDB) 3.23.aj_ag_kb $12$ (not in LMFDB) 3.23.j_ag_akb $12$ (not in LMFDB)