Properties

Label 2.16.am_cn
Base Field $\F_{2^{4}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $2$
L-polynomial:  $1 - 12 x + 65 x^{2} - 192 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.0826163580681$, $\pm0.320878822416$
Angle rank:  $2$ (numerical)
Number field:  4.0.27792.2
Galois group:  $D_{4}$
Jacobians:  4

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 118 62068 16921318 4299077952 1098243213958 281339484788212 72053442228006742 18447134402076726528 4722425255655707546902 1208929617405536715170548

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 243 4133 65599 1047365 16769139 268419989 4295058175 68720331989 1099515081843

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.27792.2.
All geometric endomorphisms are defined over $\F_{2^{4}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.16.m_cn$2$2.256.ao_ez