# Properties

 Label 4.3.ah_ba_aco_ey Base Field $\F_{3}$ Dimension $4$ Ordinary Yes $p$-rank $4$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{3}$ Dimension: $4$ L-polynomial: $( 1 - 2 x + 3 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 45 x^{5} + 27 x^{6} )$ Frobenius angles: $\pm0.0714477711956$, $\pm0.272071776080$, $\pm0.304086723985$, $\pm0.560185743604$ Angle rank: $4$ (numerical)

This isogeny class is not simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $4$ Slopes: $[0, 0, 0, 0, 1, 1, 1, 1]$

## 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 $A(\F_{q^r})$ 10 9300 621490 46500000 3863596550 261827522100 20243733754240 1813169850000000 154314037806166930 12353429416140532500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -3 13 33 89 267 673 1922 6417 20229 59993

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
 The isogeny class factors as 1.3.ac $\times$ 3.3.af_n_az 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 $\F_{3}$.

## Base change

This is a primitive isogeny class.

## Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 4.3.ad_g_ao_bc $2$ (not in LMFDB) 4.3.d_g_o_bc $2$ (not in LMFDB) 4.3.h_ba_co_ey $2$ (not in LMFDB)