Properties

Label 3.23.aw_ip_abzv
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:  $1 - 22 x + 223 x^{2} - 1347 x^{3} + 5129 x^{4} - 11638 x^{5} + 12167 x^{6}$
Frobenius angles:  $\pm0.0394215835568$, $\pm0.175002735951$, $\pm0.351893565228$
Angle rank:  $3$ (numerical)
Number field:  6.0.1392115799.1
Galois group:  $S_4\times C_2$

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
$A(\F_{q^r})$ 4513 137768351 1805348874844 21914201142006719 266505266925446872048 3243783930808944944698928 39471581442512643698256350471 480252812996839244202985639633775 5843212712169828261728714380882050364 71094324648032871498566508650751646712576

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 492 12197 279836 6433207 148019145 3404825216 78311319396 1801153175195 41426497145507

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 6.0.1392115799.1.
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.w_ip_bzv$2$(not in LMFDB)