Properties

Label 2.23.am_dc
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:  $1 - 12 x + 80 x^{2} - 276 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.218762671529$, $\pm0.34132518182$
Angle rank:  $2$ (numerical)
Number field:  4.0.168192.6
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
$A(\F_{q^r})$ 322 289156 152025538 78707106576 41438017377442 21913063512532612 11592661827690871522 6132608460735345082368 3244150810100800640088706 1716155531592944527772339716

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 546 12492 281254 6438132 148025346 3404774196 78310960318 1801152606060 41426503978146

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.