Properties

Label 2.23.am_cy
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:  $1 - 12 x + 76 x^{2} - 276 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.156924629149$, $\pm0.379300706967$
Angle rank:  $2$ (numerical)
Number field:  4.0.942336.2
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
$A(\F_{q^r})$ 318 284292 150246414 78411145104 41421021299598 21915833508260676 11593400871101108286 6132684451572789350400 3244153519445374311141726 1716155291802775268676630852

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 538 12348 280198 6435492 148044058 3404991252 78311930686 1801154110284 41426498189818

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.