Properties

Label 2.23.al_cj
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:  $1 - 11 x + 61 x^{2} - 253 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.0628794069817$, $\pm0.446825336732$
Angle rank:  $2$ (numerical)
Number field:  4.0.1179557.1
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
$A(\F_{q^r})$ 327 279585 147103893 77871412125 41384337925872 21915209201939145 11593127826326377833 6132600655234032403125 3244147080284782718553267 1716155988168640207736044800

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 531 12091 278267 6429788 148039839 3404911061 78310860643 1801150535263 41426514999486

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.