Properties

Label 3.23.ay_jw_acim
Base Field $\F_{23}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes

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Invariants

Base field:  $\F_{23}$
Dimension:  $3$
L-polynomial:  $( 1 - 9 x + 23 x^{2} )( 1 - 15 x + 98 x^{2} - 345 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.0252283536038$, $\pm0.112386341891$, $\pm0.308104979730$
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 it is unknown whether it contains a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4020 131068080 1785051927360 21884576249764800 266455388712937988100 3243480420088754908508160 39470302330561230206080853580 480250881741851255738962989100800 5843219747645175641319202733299515840 71094375101771983017935112122225134340400

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 466 12060 279458 6432000 148005292 3404714880 78311004482 1801155343860 41426526544786

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.aj $\times$ 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.sti. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{23^{6}}$.
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.ag_ao_hk$2$(not in LMFDB)
3.23.g_ao_ahk$2$(not in LMFDB)
3.23.y_jw_cim$2$(not in LMFDB)
3.23.aj_ca_akb$3$(not in LMFDB)
3.23.g_ao_ahk$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.23.ag_ao_hk$2$(not in LMFDB)
3.23.g_ao_ahk$2$(not in LMFDB)
3.23.y_jw_cim$2$(not in LMFDB)
3.23.aj_ca_akb$3$(not in LMFDB)
3.23.g_ao_ahk$3$(not in LMFDB)
3.23.j_ca_kb$6$(not in LMFDB)
3.23.aj_ag_kb$12$(not in LMFDB)
3.23.j_ag_akb$12$(not in LMFDB)