Properties

Label 3.23.ay_jx_aciv
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:  $( 1 - 9 x + 23 x^{2} )( 1 - 15 x + 99 x^{2} - 345 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.0783210629050$, $\pm0.112386341891$, $\pm0.297557123995$
Angle rank:  $3$ (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
$A(\F_{q^r})$ 4035 131690295 1791800160660 21924256618472175 266613847783369918800 3243961753187570465632560 39471541480625178516001929165 480254095454378769774496163919375 5843229593458532668083265549574417940 71094408420642952346582854228973792121600

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 468 12105 279964 6435825 148027257 3404821770 78311528516 1801158378795 41426545959603

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.aj $\times$ 2.23.ap_dv 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 is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.23.ag_an_ht$2$(not in LMFDB)
3.23.g_an_aht$2$(not in LMFDB)
3.23.y_jx_civ$2$(not in LMFDB)