Properties

Label 3.23.az_kq_acob
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:  $( 1 - 7 x + 23 x^{2} )( 1 - 9 x + 23 x^{2} )^{2}$
Frobenius angles:  $\pm0.112386341891$, $\pm0.112386341891$, $\pm0.239612957690$
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
$A(\F_{q^r})$ 3825 129128175 1790119828800 21970761907111875 266887498406748676875 3244810077586313421926400 39472989695789538488552414325 480253970531619858359397768316875 5843220773624882438138013139444670400 71094382589486502645510538066686028104375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 457 12092 280557 6442429 148065964 3404946691 78311508149 1801155660116 41426530907857

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.aj 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.al_y_cj$2$(not in LMFDB)
3.23.ah_am_jl$2$(not in LMFDB)
3.23.h_am_ajl$2$(not in LMFDB)
3.23.l_y_acj$2$(not in LMFDB)
3.23.z_kq_cob$2$(not in LMFDB)
3.23.c_s_i$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.23.al_y_cj$2$(not in LMFDB)
3.23.ah_am_jl$2$(not in LMFDB)
3.23.h_am_ajl$2$(not in LMFDB)
3.23.l_y_acj$2$(not in LMFDB)
3.23.z_kq_cob$2$(not in LMFDB)
3.23.c_s_i$3$(not in LMFDB)
3.23.ah_cg_ajl$4$(not in LMFDB)
3.23.h_cg_jl$4$(not in LMFDB)
3.23.aq_fo_abfo$6$(not in LMFDB)
3.23.ac_s_ai$6$(not in LMFDB)
3.23.q_fo_bfo$6$(not in LMFDB)