# Properties

 Label 3.23.ax_jl_acfy 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: $( 1 - 7 x + 23 x^{2} )( 1 - 8 x + 23 x^{2} )^{2}$ Frobenius angles: $\pm0.186011988595$, $\pm0.186011988595$, $\pm0.239612957690$ 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 does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4352 138149888 1834326029312 22112551793852416 267216870355299580672 3245251242006322425626624 39472445038268992026527026432 480247704656201591283019658821632 5843194311526475086466814808153447424 71094301724427172337293757030955705171968

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 491 12388 282359 6450371 148086092 3404899709 78310486415 1801147503244 41426483787971

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.ai 2 $\times$ 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: 1.23.ai 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-7})$$$)$ 1.23.ah : $$\Q(\sqrt{-43})$$.
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_v_bi $2$ (not in LMFDB) 3.23.ah_f_ew $2$ (not in LMFDB) 3.23.h_f_aew $2$ (not in LMFDB) 3.23.j_v_abi $2$ (not in LMFDB) 3.23.x_jl_cfy $2$ (not in LMFDB) 3.23.b_i_dd $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.23.aj_v_bi $2$ (not in LMFDB) 3.23.ah_f_ew $2$ (not in LMFDB) 3.23.h_f_aew $2$ (not in LMFDB) 3.23.j_v_abi $2$ (not in LMFDB) 3.23.x_jl_cfy $2$ (not in LMFDB) 3.23.b_i_dd $3$ (not in LMFDB) 3.23.ah_bp_aew $4$ (not in LMFDB) 3.23.h_bp_ew $4$ (not in LMFDB) 3.23.ap_eq_azf $6$ (not in LMFDB) 3.23.ab_i_add $6$ (not in LMFDB) 3.23.p_eq_zf $6$ (not in LMFDB)