Properties

Label 2.23.am_cw
Base Field $\F_{23}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{23}$
Dimension:  $2$
Weil polynomial:  $1 - 12 x + 74 x^{2} - 276 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.127841060579$, $\pm0.392728894411$
Angle rank:  $2$ (numerical)
Number field:  4.0.18432.2
Galois group:  $C_4$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 316 281872 149359612 78256687104 41407899346876 21915733620886288 11593492395819276412 6132693683563722473472 3244154689703471031918652 1716155653883442087178573072

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 534 12276 279646 6433452 148043382 3405018132 78312048574 1801154760012 41426506930134

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.