# Properties

 Label 3.23.ay_ka_acjw 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: $( 1 - 9 x + 23 x^{2} )( 1 - 8 x + 23 x^{2} )( 1 - 7 x + 23 x^{2} )$ Frobenius angles: $\pm0.112386341891$, $\pm0.186011988595$, $\pm0.239612957690$ Angle rank: $3$ (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 $A(\F_{q^r})$ 4080 133562880 1812088131840 22041542836684800 267052133601674084400 3245030652299237537218560 39472717366089844834779768720 480250837583691795543968260300800 5843207542560698919317652488486511360 71094342156945340166822404397294527910400

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 0 474 12240 281458 6446400 148076028 3404923200 78310997282 1801151581680 41426507347914

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.aj $\times$ 1.23.ai $\times$ 1.23.ah and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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_w_bs $2$ (not in LMFDB) 3.23.ai_e_fg $2$ (not in LMFDB) 3.23.ag_ak_iu $2$ (not in LMFDB) 3.23.g_ak_aiu $2$ (not in LMFDB) 3.23.i_e_afg $2$ (not in LMFDB) 3.23.k_w_abs $2$ (not in LMFDB) 3.23.y_ka_cjw $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.23.ak_w_bs $2$ (not in LMFDB) 3.23.ai_e_fg $2$ (not in LMFDB) 3.23.ag_ak_iu $2$ (not in LMFDB) 3.23.g_ak_aiu $2$ (not in LMFDB) 3.23.i_e_afg $2$ (not in LMFDB) 3.23.k_w_abs $2$ (not in LMFDB) 3.23.y_ka_cjw $2$ (not in LMFDB)