Properties

Label 3.23.aw_ir_acao
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:  $1 - 22 x + 225 x^{2} - 1366 x^{3} + 5175 x^{4} - 11638 x^{5} + 12167 x^{6}$
Frobenius angles:  $\pm0.0404981459123$, $\pm0.210373719318$, $\pm0.328791241931$
Angle rank:  $3$ (numerical)
Number field:  6.0.1108246464.1
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
$A(\F_{q^r})$ 4542 138957948 1816458854922 21960510012207216 266581691987972792142 3243596627864919477833244 39470059593764327916287932458 480248461449294341158084920880896 5843207861674666241771931654862245654 71094335019665046439306034548883099739708

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 496 12272 280428 6435052 148010596 3404693938 78310609820 1801151680046 41426503189036

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 6.0.1108246464.1.
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_ir_cao$2$(not in LMFDB)