Properties

Label 2.1024.aeq_iir
Base Field $\F_{2^{10}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{2^{10}}$
Dimension:  $2$
L-polynomial:  $1 - 120 x + 5633 x^{2} - 122880 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0200575241716$, $\pm0.159551478631$
Angle rank:  $2$ (numerical)
Number field:  4.0.55299600.1
Galois group:  $D_{4}$

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 a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 931210 1096229724100 1152847676549117290 1208924556634616993337600 1267650589202740779222508110250 1329227995937536190953445652709404100 1393796574910522748993624909119469196175690 1461501637330292695415125575809973657831271449600 1532495540865832790070410180236596568659082602595608010 1606938044258987125494584469978971055864150111168477442562500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 905 1045443 1073673065 1099510479103 1125899897050025 1152921504739224003 1180591620719409286985 1208925819614124410246143 1237940039285334983296819145 1267650600228226916547477405123

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.55299600.1.
All geometric endomorphisms are defined over $\F_{2^{10}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.1024.eq_iir$2$(not in LMFDB)