Properties

Label 2.11.ah_bd
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:  $1 - 7 x + 29 x^{2} - 77 x^{3} + 121 x^{4}$
Frobenius angles:  $\pm0.162126013132$, $\pm0.441671623734$
Angle rank:  $2$ (numerical)
Number field:  4.0.196245.1
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
$A(\F_{q^r})$ 67 15745 1820725 213329005 25941832912 3145275126625 380071732355137 45952810361641845 5559718341588279775 672744727725974368000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 131 1367 14571 161080 1775423 19503685 214373251 2357863307 25937221526

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.