# Properties

 Label 3.23.aba_li_acsy Base Field $\F_{23}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $( 1 - 8 x + 23 x^{2} )( 1 - 9 x + 23 x^{2} )^{2}$ Frobenius angles: $\pm0.112386341891$, $\pm0.112386341891$, $\pm0.186011988595$ 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 does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3600 125452800 1775575468800 21946123203840000 266921851464714690000 3245204608356438746726400 39474492984863372442103628400 480257414928376694985956152320000 5843223920785054029381351132026630400 71094369678538432325821958680312461120000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 442 11992 280242 6443258 148083964 3405076358 78312069794 1801156630216 41426523384682

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.aj 2 $\times$ 1.23.ai and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: 1.23.aj 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-11})$$$)$ 1.23.ai : $$\Q(\sqrt{-7})$$.
All geometric endomorphisms are defined over $\F_{23}$.

## 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.ak_g_hg $2$ (not in LMFDB) 3.23.ai_am_ku $2$ (not in LMFDB) 3.23.i_am_aku $2$ (not in LMFDB) 3.23.k_g_ahg $2$ (not in LMFDB) 3.23.ba_li_csy $2$ (not in LMFDB) 3.23.b_j_aby $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.23.ak_g_hg $2$ (not in LMFDB) 3.23.ai_am_ku $2$ (not in LMFDB) 3.23.i_am_aku $2$ (not in LMFDB) 3.23.k_g_ahg $2$ (not in LMFDB) 3.23.ba_li_csy $2$ (not in LMFDB) 3.23.b_j_aby $3$ (not in LMFDB) 3.23.ai_cg_aku $4$ (not in LMFDB) 3.23.i_cg_ku $4$ (not in LMFDB) 3.23.ar_fx_abhu $6$ (not in LMFDB) 3.23.ab_j_by $6$ (not in LMFDB) 3.23.r_fx_bhu $6$ (not in LMFDB)