Properties

Label 2.11.ai_bj
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:  $1 - 8 x + 35 x^{2} - 88 x^{3} + 121 x^{4}$
Frobenius angles:  $\pm0.167863583547$, $\pm0.388927483238$
Angle rank:  $2$ (numerical)
Number field:  4.0.62352.1
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
$A(\F_{q^r})$ 61 15433 1859524 215583577 25923018781 3140788102672 380007301885909 45958600415667753 5559909320049903844 672737694627725025673

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 128 1396 14724 160964 1772894 19500380 214400260 2357944300 25936950368

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.