Properties

Label 3.23.aba_li_acsy
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:  $( 1 - 8 x + 23 x^{2} )( 1 - 9 x + 23 x^{2} )^{2}$
Frobenius angles:  $\pm0.112386341891$, $\pm0.112386341891$, $\pm0.186011988595$
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
$A(\F_{q^r})$ 3600 125452800 1775575468800 21946123203840000 266921851464714690000 3245204608356438746726400 39474492984863372442103628400 480257414928376694985956152320000 5843223920785054029381351132026630400 71094369678538432325821958680312461120000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 442 11992 280242 6443258 148083964 3405076358 78312069794 1801156630216 41426523384682

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.aj 2 $\times$ 1.23.ai 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.ak_g_hg$2$(not in LMFDB)
3.23.ai_am_ku$2$(not in LMFDB)
3.23.i_am_aku$2$(not in LMFDB)
3.23.k_g_ahg$2$(not in LMFDB)
3.23.ba_li_csy$2$(not in LMFDB)
3.23.b_j_aby$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.23.ak_g_hg$2$(not in LMFDB)
3.23.ai_am_ku$2$(not in LMFDB)
3.23.i_am_aku$2$(not in LMFDB)
3.23.k_g_ahg$2$(not in LMFDB)
3.23.ba_li_csy$2$(not in LMFDB)
3.23.b_j_aby$3$(not in LMFDB)
3.23.ai_cg_aku$4$(not in LMFDB)
3.23.i_cg_ku$4$(not in LMFDB)
3.23.ar_fx_abhu$6$(not in LMFDB)
3.23.ab_j_by$6$(not in LMFDB)
3.23.r_fx_bhu$6$(not in LMFDB)