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

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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.

Point counts of the abelian variety

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

Point counts of the (virtual) curve

$r$ 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:
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.
TwistExtension DegreeCommon 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.
TwistExtension DegreeCommon 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)