Properties

Label 2.4.ad_h
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:  $1-3x+7x^{2}-12x^{3}+16x^{4}$
Frobenius angles:  $\pm0.190783854037$, $\pm0.524117187371$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}, \sqrt{13})\)
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
$A(\F_{q^r})$ 9 351 4212 63531 1141299 17740944 268402689 4264772499 68719584492 1099012730751

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 22 65 250 1112 4327 16382 65074 262145 1048102

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.