Properties

Label 2.11.ai_bh
Base Field $\F_{11}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{11}$
Dimension:  $2$
Weil polynomial:  $1 - 8 x + 33 x^{2} - 88 x^{3} + 121 x^{4}$
Frobenius angles:  $\pm0.110710227191$, $\pm0.414323386517$
Angle rank:  $2$ (numerical)
Number field:  4.0.5225.1
Galois group:  $D_4$

This isogeny class is simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

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
$A(\F_{q^r})$ 59 14809 1793600 212079689 25833279859 3140550553600 380044419083339 45959060061139529 5559995444950145600 672750358072070821609

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 124 1348 14484 160404 1772758 19502284 214402404 2357980828 25937438604

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.