Properties

Label 2.11.ai_bg
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:  $1 - 8 x + 32 x^{2} - 88 x^{3} + 121 x^{4}$
Frobenius angles:  $\pm0.0750991438595$, $\pm0.424900856141$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(i, \sqrt{6})\)
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
$A(\F_{q^r})$ 58 14500 1760938 210250000 25769191258 3138431750500 379935240802378 45953639424000000 5559842595347832058 672749994932236862500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 122 1324 14358 160004 1771562 19496684 214377118 2357916004 25937424602

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.