Properties

Label 2.1024.aev_iuz
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:  $1 - 125 x + 5953 x^{2} - 128000 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0347939497301$, $\pm0.0913596598443$
Angle rank:  $2$ (numerical)
Number field:  4.0.400025.1
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
$A(\F_{q^r})$ 926405 1095617505275 1152809034947817620 1208922784703586848280275 1267650525453700923264392560125 1329227994195862941338804718669214400 1393796574884079420247731634646587198882445 1461501637330961327368198708122995915363073042275 1532495540865914485901113316483485111635318800364188180 1606938044258991713168567548709642114029173237990191603296875

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 900 1044858 1073637075 1099508867538 1125899840429500 1152921503228563263 1180591620697010916300 1208925819614677489634658 1237940039285400976663307475 1267650600228230535584128555498

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.400025.1.
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.ev_iuz$2$(not in LMFDB)