Properties

Label 2.4.a_ad
Base Field $\F_{2^2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $1-3x^{2}+16x^{4}$
Frobenius angles:  $\pm0.18882135323$, $\pm0.81117864677$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-5}, \sqrt{11})\)
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
$A(\F_{q^r})$ 14 196 4214 78400 1046654 17757796 268449734 4292870400 68719640654 1095484595716

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 11 65 303 1025 4331 16385 65503 262145 1044731

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.