Properties

Label 3.23.ax_jh_acer
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:  $1 - 23 x + 241 x^{2} - 1473 x^{3} + 5543 x^{4} - 12167 x^{5} + 12167 x^{6}$
Frobenius angles:  $\pm0.0674379021370$, $\pm0.168826572348$, $\pm0.311698514191$
Angle rank:  $3$ (numerical)
Number field:  6.0.173393831.1
Galois group:  $A_4\times C_2$

This isogeny class is simple and geometrically 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
$A(\F_{q^r})$ 4289 135596735 1807498648799 21962411298569975 266679478378081493999 3244036783688524877654015 39471465782985360090139173376 480252672097995461155376821454375 5843220513641392795144039931057467793 71094368595923794346330351102325782734175

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 483 12211 280451 6437411 148030683 3404815240 78311296419 1801155579973 41426522753843

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 6.0.173393831.1.
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.x_jh_cer$2$(not in LMFDB)