Properties

Label 2.23.am_cu
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:  $1 - 12 x + 72 x^{2} - 276 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.095603857529$, $\pm0.404396142471$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(i, \sqrt{10})\)
Galois group:  $V_4$

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
$A(\F_{q^r})$ 314 279460 148474586 78097891600 41391692364794 21914624696975140 11593380278594010266 6132675219602112921600 3244153234658230621747514 1716155831334506630544686500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 530 12204 279078 6430932 148035890 3404985204 78311812798 1801153952172 41426511213650

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.