Properties

Label 2.11.ah_be
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:  $1 - 7 x + 30 x^{2} - 77 x^{3} + 121 x^{4}$
Frobenius angles:  $\pm0.183470593443$, $\pm0.430420419745$
Angle rank:  $2$ (numerical)
Number field:  4.0.39593.1
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
$A(\F_{q^r})$ 68 16048 1849328 214465472 25947340108 3144123903232 380029698717212 45951475832008448 5559601338333581552 672737920931822176048

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 133 1388 14649 161115 1774774 19501529 214367025 2357813684 25936959093

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.