Properties

 Label 3.23.ax_ji_acfb Base Field $\F_{23}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes

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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4303 136185647 1813248244132 21987555798375011 266718802742136815993 3243851264726561711301872 39469891272095207054481770719 480246501341871617048478345404075 5843205130433243487209813955678625852 71094347136938733286581902100190653252767

 $r$ 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.
 Twist Extension Degree Common base change 3.23.x_ji_cfb $2$ (not in LMFDB)