Properties

Label 3.23.ax_ji_acfb
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:  $1 - 23 x + 242 x^{2} - 1483 x^{3} + 5566 x^{4} - 12167 x^{5} + 12167 x^{6}$
Frobenius angles:  $\pm0.0483565798313$, $\pm0.203970483688$, $\pm0.292048023943$
Angle rank:  $3$ (numerical)
Number field:  6.0.88032176.1
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
$A(\F_{q^r})$ 4303 136185647 1813248244132 21987555798375011 266718802742136815993 3243851264726561711301872 39469891272095207054481770719 480246501341871617048478345404075 5843205130433243487209813955678625852 71094347136938733286581902100190653252767

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 485 12250 280773 6438361 148022216 3404679419 78310290197 1801150838146 41426510249745

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 6.0.88032176.1.
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_ji_cfb$2$(not in LMFDB)