Properties

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

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Invariants

Base field:  $\F_{2^{10}}$
Dimension:  $2$
L-polynomial:  $1 - 120 x + 5641 x^{2} - 122880 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0655983852739$, $\pm0.146345352353$
Angle rank:  $2$ (numerical)
Number field:  4.0.12049296.1
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
$A(\F_{q^r})$ 931218 1096246591524 1152850769309131650 1208924864956269785608704 1267650611630668828237348052178 1329227997269022088804127174814022500 1393796574978681644807548118322731720169858 1461501637333394720627659237661675077226665887744 1532495540865960606567810317334614901093329335420664850 1606938044258991946053264353417843548338083237768198259243684

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 905 1045459 1073675945 1099510759519 1125899916970025 1152921505894103923 1180591620777142117385 1208925819616690345361599 1237940039285438232641168585 1267650600228230719297761288979

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.12049296.1.
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_iiz$2$(not in LMFDB)