Properties

Label 2.11.aj_bn
Base Field $\F_{11}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{11}$
Dimension:  $2$
Weil polynomial:  $1 - 9 x + 39 x^{2} - 99 x^{3} + 121 x^{4}$
Frobenius angles:  $\pm0.100899808413$, $\pm0.366706655625$
Angle rank:  $2$ (numerical)
Number field:  4.0.26533.1
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
$A(\F_{q^r})$ 53 14257 1807247 213698173 25827579248 3136150056793 379889663866283 45961032196550133 5560271234957193833 672754159756611135232

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 119 1359 14595 160368 1770275 19494345 214411603 2358097785 25937585174

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.