Properties

Label 2.1024.aeq_iiv
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:  $1 - 120 x + 5637 x^{2} - 122880 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0465577460529$, $\pm0.153694224197$
Angle rank:  $2$ (numerical)
Number field:  4.0.148733200.1
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
$A(\F_{q^r})$ 931214 1096238157796 1152849222928853894 1208924710830625721915200 1267650600427513433128114212254 1329227996605045932098933142443255236 1393796574944807089426295342845387121303894 1461501637331862619889241368314470673068944467200 1532495540865898174717082998338799220635769025026071214 1606938044258989636911256854008905724430248227621980494260516

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 905 1045451 1073674505 1099510619343 1125899907019625 1152921505318196411 1180591620748449252905 1208925819615423021334303 1237940039285387800593778505 1267650600228228897705906969131

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.148733200.1.
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_iiv$2$(not in LMFDB)