# Properties

 Label 3.23.abb_ma_acxv 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: $( 1 - 9 x + 23 x^{2} )^{3}$ Frobenius angles: $\pm0.112386341891$, $\pm0.112386341891$, $\pm0.112386341891$ Angle rank: $1$ (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 $A(\F_{q^r})$ 3375 121287375 1754049816000 21875648690671875 266757296587533703125 3244984021819186454016000 39474765326813393907880360875 480260547919212498486209874796875 5843237151886323572628557017104456000 71094410111095246794693772521401657484375

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -3 425 11844 279341 6439287 148073900 3405099849 78312580661 1801160708652 41426546944625

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.aj 3 and its endomorphism algebra is $\mathrm{M}_{3}($$$\Q(\sqrt{-11})$$$)$
All geometric endomorphisms are defined over $\F_{23}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 3.23.aj_am_md $2$ (not in LMFDB) 3.23.j_am_amd $2$ (not in LMFDB) 3.23.bb_ma_cxv $2$ (not in LMFDB) 3.23.a_a_aee $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.23.aj_am_md $2$ (not in LMFDB) 3.23.j_am_amd $2$ (not in LMFDB) 3.23.bb_ma_cxv $2$ (not in LMFDB) 3.23.a_a_aee $3$ (not in LMFDB) 3.23.aj_cg_amd $4$ (not in LMFDB) 3.23.j_cg_md $4$ (not in LMFDB) 3.23.as_gg_abka $6$ (not in LMFDB) 3.23.a_a_ee $6$ (not in LMFDB) 3.23.s_gg_bka $6$ (not in LMFDB)