Properties

Label 3.23.ax_jh_aces
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:  $( 1 - 8 x + 23 x^{2} )( 1 - 15 x + 98 x^{2} - 345 x^{3} + 529 x^{4} )$
  $1 - 23 x + 241 x^{2} - 1474 x^{3} + 5543 x^{4} - 12167 x^{5} + 12167 x^{6}$
Frobenius angles:  $\pm0.0252283536038$, $\pm0.186011988595$, $\pm0.308104979730$
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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $4288$ $135569408$ $1806958037248$ $21955079523926016$ $266619757351864728128$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $1$ $483$ $12208$ $280359$ $6435971$ $148015356$ $3404691389$ $78310493615$ $1801151265424$ $41426502984843$

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 $\F_{23^{6}}$.

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.ai $\times$ 2.23.ap_du and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
Endomorphism algebra over $\overline{\F}_{23}$
The base change of $A$ to $\F_{23^{6}}$ is 1.148035889.abgac 2 $\times$ 1.148035889.bhqk. The endomorphism algebra for each factor is:
Remainder of endomorphism lattice by field

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.ah_b_dq$2$(not in LMFDB)
3.23.h_b_adq$2$(not in LMFDB)
3.23.x_jh_ces$2$(not in LMFDB)
3.23.ai_ca_aiy$3$(not in LMFDB)
3.23.h_b_adq$3$(not in LMFDB)

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

TwistExtension degreeCommon base change
3.23.ah_b_dq$2$(not in LMFDB)
3.23.h_b_adq$2$(not in LMFDB)
3.23.x_jh_ces$2$(not in LMFDB)
3.23.ai_ca_aiy$3$(not in LMFDB)
3.23.h_b_adq$3$(not in LMFDB)
3.23.ai_ca_aiy$6$(not in LMFDB)
3.23.ah_b_dq$6$(not in LMFDB)
3.23.i_ca_iy$6$(not in LMFDB)
3.23.ai_ag_iy$12$(not in LMFDB)
3.23.i_ag_aiy$12$(not in LMFDB)