# Properties

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

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $( 1 - 9 x + 23 x^{2} )( 1 - 7 x + 23 x^{2} )^{2}$ Frobenius angles: $\pm0.112386341891$, $\pm0.239612957690$, $\pm0.239612957690$ 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 $A(\F_{q^r})$ 4335 137475855 1826931579840 22066288666668675 267017763776291771925 3244636142677552911298560 39471214144636089055811753835 480247393234107545944812499545675 5843204395409348639061291504154647360 71094355067888412483703841674889995754775

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 489 12340 281773 6445571 148058028 3404793533 78310435637 1801150611580 41426514871089

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.aj $\times$ 1.23.ah 2 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 : $$\Q(\sqrt{-11})$$. 1.23.ah 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-43})$$$)$
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.aj_u_bb $2$ (not in LMFDB) 3.23.af_ai_id $2$ (not in LMFDB) 3.23.f_ai_aid $2$ (not in LMFDB) 3.23.j_u_abb $2$ (not in LMFDB) 3.23.x_jk_cfr $2$ (not in LMFDB) 3.23.ac_ao_dk $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.23.aj_u_bb $2$ (not in LMFDB) 3.23.af_ai_id $2$ (not in LMFDB) 3.23.f_ai_aid $2$ (not in LMFDB) 3.23.j_u_abb $2$ (not in LMFDB) 3.23.x_jk_cfr $2$ (not in LMFDB) 3.23.ac_ao_dk $3$ (not in LMFDB) 3.23.aj_ba_abb $4$ (not in LMFDB) 3.23.j_ba_bb $4$ (not in LMFDB) 3.23.aq_ei_avk $6$ (not in LMFDB) 3.23.c_ao_adk $6$ (not in LMFDB) 3.23.q_ei_vk $6$ (not in LMFDB)