# Properties

 Label 3.23.ay_jz_acjn Base Field $\F_{23}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $( 1 - 9 x + 23 x^{2} )( 1 - 15 x + 101 x^{2} - 345 x^{3} + 529 x^{4} )$ Frobenius angles: $\pm0.112386341891$, $\pm0.144663500024$, $\pm0.268275520367$ Angle rank: $3$ (numerical)

This isogeny class is not 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 does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4065 132937695 1805318190540 22002739240712175 266912217466704901200 3244736599417922444454960 39472741683008465581121151435 480253970332403578458274201779375 5843222510746695910142084840628206460 71094384915721897391615761484393173881600

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 0 472 12195 280964 6443025 148062613 3404925300 78311508116 1801156195575 41426532263347

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.aj $\times$ 2.23.ap_dx and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ag_al_il $2$ (not in LMFDB) 3.23.g_al_ail $2$ (not in LMFDB) 3.23.y_jz_cjn $2$ (not in LMFDB)