Properties

Label 2.1024.aeo_idx
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:  $1 - 118 x + 5509 x^{2} - 120832 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0409105324456$, $\pm0.175390895296$
Angle rank:  $2$ (numerical)
Number field:  4.0.1888625.2
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
$A(\F_{q^r})$ 933136 1096468392896 1152862083407398096 1208925176318895947928320 1267650609724655848127672820496 1329227996451908141333777675583022016 1393796574918948215703783444183149873657296 1461501637330326810479494102506333267734394629120 1532495540865832538167206981719411263112886931506789136 1606938044258987428394449173710746464255390687700988896238016

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 907 1045671 1073686483 1099511042703 1125899915277147 1152921505185370551 1180591620726545934883 1208925819614152629565983 1237940039285334779811032107 1267650600228227155493338866631

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.1888625.2.
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.eo_idx$2$(not in LMFDB)