Properties

Label 2.4.ab_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:  $1-x-3x^{2}-4x^{3}+16x^{4}$
Frobenius angles:  $\pm0.0862360434115$, $\pm0.752902710078$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}, \sqrt{5})\)
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
$A(\F_{q^r})$ 9 171 2916 69939 988749 16842816 272594709 4280336739 69130081476 1101267647451

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 10 43 274 964 4111 16636 65314 263707 1050250

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.