Properties

Label 2.23.am_de
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:  $( 1 - 6 x + 23 x^{2} )^{2}$
Frobenius angles:  $\pm0.284877382774$, $\pm0.284877382774$
Angle rank:  $1$ (numerical)

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
$A(\F_{q^r})$ 324 291600 152917956 78848640000 41441895501444 21910222361840400 11592041781277242756 6132554332457379840000 3244152837831332022368964 1716156779757490607324490000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 550 12564 281758 6438732 148006150 3404592084 78310269118 1801153731852 41426534107750

Decomposition

1.23.ag 2

Base change

This is a primitive isogeny class.