Properties

Label 3.23.ax_jg_aceh
Base field $\F_{23}$
Dimension $3$
$p$-rank $3$
Ordinary yes
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes

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Invariants

Base field:  $\F_{23}$
Dimension:  $3$
L-polynomial:  $( 1 - 5 x + 23 x^{2} )( 1 - 9 x + 23 x^{2} )^{2}$
  $1 - 23 x + 240 x^{2} - 1463 x^{3} + 5520 x^{4} - 12167 x^{5} + 12167 x^{6}$
Frobenius angles:  $\pm0.112386341891$, $\pm0.112386341891$, $\pm0.325452467839$
Angle rank:  $2$ (numerical)

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $4275$ $135008775$ $1801755316800$ $21936971685481875$ $266634802450805675625$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $1$ $481$ $12172$ $280125$ $6436331$ $148037164$ $3404933477$ $78312227861$ $1801160644036$ $41426544006361$

Jacobians and polarizations

This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{23}$.

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.aj 2 $\times$ 1.23.af and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

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.an_ci_ahl$2$(not in LMFDB)
3.23.af_am_gt$2$(not in LMFDB)
3.23.f_am_agt$2$(not in LMFDB)
3.23.n_ci_hl$2$(not in LMFDB)
3.23.x_jg_ceh$2$(not in LMFDB)
3.23.e_bk_eu$3$(not in LMFDB)

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
3.23.an_ci_ahl$2$(not in LMFDB)
3.23.af_am_gt$2$(not in LMFDB)
3.23.f_am_agt$2$(not in LMFDB)
3.23.n_ci_hl$2$(not in LMFDB)
3.23.x_jg_ceh$2$(not in LMFDB)
3.23.e_bk_eu$3$(not in LMFDB)
3.23.af_cg_agt$4$(not in LMFDB)
3.23.f_cg_gt$4$(not in LMFDB)
3.23.ao_ew_abbc$6$(not in LMFDB)
3.23.ae_bk_aeu$6$(not in LMFDB)
3.23.o_ew_bbc$6$(not in LMFDB)