Properties

Label 2.23.al_cq
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:  $1 - 11 x + 68 x^{2} - 253 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.162255762163$, $\pm0.411666868096$
Angle rank:  $2$ (numerical)
Number field:  4.0.2029896.1
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
$A(\F_{q^r})$ 334 287908 149932600 78313279264 41421476307754 21917875540705600 11593568288441234506 6132662894255511233664 3244148608497113137240600 1716155133197554058823493828

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 545 12322 279849 6435563 148057850 3405040421 78311655409 1801151383726 41426494361225

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.