Properties

Label 2.23.an_dk
Base Field $\F_{23}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{23}$
Dimension:  $2$
Weil polynomial:  $( 1 - 7 x + 23 x^{2} )( 1 - 6 x + 23 x^{2} )$
Frobenius angles:  $\pm0.23961295769$, $\pm0.284877382774$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 306 284580 152200728 78874192800 41460751050246 21913124165916480 11592229009616993862 6132540030039359913600 3244147612084323349827192 1716156134601829936571664900

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 537 12506 281849 6441661 148025754 3404647075 78310086481 1801150830518 41426518534257

Decomposition

1.23.ah $\times$ 1.23.ag

Base change

This is a primitive isogeny class.