Properties

Label 2.23.an_dh
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:  $1 - 13 x + 85 x^{2} - 299 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.16692190462$, $\pm0.337099187115$
Angle rank:  $2$ (numerical)
Number field:  4.0.272597.1
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
$A(\F_{q^r})$ 303 280881 150749469 78596402301 41436887174448 21914633167635897 11593009791974717409 6132657490305172851573 3244155682177054974644523 1716155771266029109654031616

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 531 12389 280859 6437956 148035951 3404876395 78311586403 1801155311033 41426509763646

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.