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

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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.

Point counts of the abelian variety

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

Point counts of the (virtual) curve

$r$ 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.
TwistExtension DegreeCommon 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)