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

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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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3375 121287375 1754049816000 21875648690671875 266757296587533703125 3244984021819186454016000 39474765326813393907880360875 480260547919212498486209874796875 5843237151886323572628557017104456000 71094410111095246794693772521401657484375

Point counts of the (virtual) curve

$r$ 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.
TwistExtension DegreeCommon 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.
TwistExtension DegreeCommon 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)