Properties

Label 2.23.an_df
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:  $1 - 13 x + 83 x^{2} - 299 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.130958063173$, $\pm0.355407705965$
Angle rank:  $2$ (numerical)
Number field:  4.0.482013.2
Galois group:  $D_4$

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
$A(\F_{q^r})$ 301 278425 149784523 78405872125 41416808880496 21914146000640425 11593204995131561767 6132692377092556351125 3244158926094022730531017 1716156041496813104283424000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 527 12311 280179 6434836 148032659 3404933725 78312031891 1801157112053 41426516286782

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.