Properties

Label 2.23.al_ck
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:  $1 - 11 x + 62 x^{2} - 253 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.0820306336664$, $\pm0.442438013535$
Angle rank:  $2$ (numerical)
Number field:  4.0.432117.2
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
$A(\F_{q^r})$ 328 280768 147506848 77937827584 41391767028088 21916218179623936 11593307157017672344 6132625650673352137728 3244149373460302602369952 1716156156365510450971933888

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 533 12124 278505 6430943 148046654 3404963729 78311179825 1801151808436 41426519059613

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.