Properties

Label 3.23.ax_jk_acfr
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:  $( 1 - 9 x + 23 x^{2} )( 1 - 7 x + 23 x^{2} )^{2}$
Frobenius angles:  $\pm0.112386341891$, $\pm0.239612957690$, $\pm0.239612957690$
Angle rank:  $2$ (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 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
$A(\F_{q^r})$ 4335 137475855 1826931579840 22066288666668675 267017763776291771925 3244636142677552911298560 39471214144636089055811753835 480247393234107545944812499545675 5843204395409348639061291504154647360 71094355067888412483703841674889995754775

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 489 12340 281773 6445571 148058028 3404793533 78310435637 1801150611580 41426514871089

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.aj $\times$ 1.23.ah 2 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
3.23.aj_u_bb$2$(not in LMFDB)
3.23.af_ai_id$2$(not in LMFDB)
3.23.f_ai_aid$2$(not in LMFDB)
3.23.j_u_abb$2$(not in LMFDB)
3.23.x_jk_cfr$2$(not in LMFDB)
3.23.ac_ao_dk$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.23.aj_u_bb$2$(not in LMFDB)
3.23.af_ai_id$2$(not in LMFDB)
3.23.f_ai_aid$2$(not in LMFDB)
3.23.j_u_abb$2$(not in LMFDB)
3.23.x_jk_cfr$2$(not in LMFDB)
3.23.ac_ao_dk$3$(not in LMFDB)
3.23.aj_ba_abb$4$(not in LMFDB)
3.23.j_ba_bb$4$(not in LMFDB)
3.23.aq_ei_avk$6$(not in LMFDB)
3.23.c_ao_adk$6$(not in LMFDB)
3.23.q_ei_vk$6$(not in LMFDB)