Properties

Label 2.4.a_ah
Base Field $\F_{2^2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $1-7x^{2}+16x^{4}$
Frobenius angles:  $\pm0.0804306232552$, $\pm0.919569376745$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(i, \sqrt{15})\)
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 is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 10 100 4090 57600 1050250 16728100 268465690 4324377600 68719562410 1103025062500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 3 65 223 1025 4083 16385 65983 262145 1051923

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.