Properties

Label 2.23.al_cp
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:  $1 - 11 x + 67 x^{2} - 253 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.150354367139$, $\pm0.417487041857$
Angle rank:  $2$ (numerical)
Number field:  4.0.2241053.1
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
$A(\F_{q^r})$ 333 286713 149527323 78253439229 41418293691888 21918113794710441 11593613907778242519 6132666771128254947093 3244149564556170503471337 1716155370596801235121913088

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 543 12289 279635 6435068 148059459 3405053819 78311704915 1801151914531 41426500091838

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.