Properties

Label 2.23.ap_dy
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:  $( 1 - 8 x + 23 x^{2} )( 1 - 7 x + 23 x^{2} )$
Frobenius angles:  $\pm0.186011988595$, $\pm0.23961295769$
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
$A(\F_{q^r})$ 272 269824 150256064 78811273216 41484954325232 21918691085541376 11592857726482833968 6132569710324332847104 3244144133641633910077376 1716155177787549343704538624

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 509 12348 281625 6445419 148063358 3404831733 78310465489 1801148899284 41426495437589

Decomposition

1.23.ai $\times$ 1.23.ah

Base change

This is a primitive isogeny class.