Properties

Label 2.11.aj_bm
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:  $1 - 9 x + 38 x^{2} - 99 x^{3} + 121 x^{4}$
Frobenius angles:  $\pm0.0468428922585$, $\pm0.380176225592$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}, \sqrt{17})\)
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
$A(\F_{q^r})$ 52 13936 1769872 211214016 25719331612 3132446896384 379744766941228 45953547054914304 5559917317647236752 672742381710223208176

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 117 1332 14425 159693 1768182 19486911 214376689 2357947692 25937131077

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.