Properties

Label 2.1024.aeq_ijb
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:  $1 - 120 x + 5643 x^{2} - 122880 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0749063474884$, $\pm0.141684297189$
Angle rank:  $2$ (numerical)
Number field:  4.0.4227025.2
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
$A(\F_{q^r})$ 931220 1096250808400 1152851542499473580 1208924941992705070830400 1267650617224140053772000090500 1329227997599685349692970745087736400 1393796574995465372107529232072132202692380 1461501637334146613976495411198052386012017030400 1532495540865990719441462574729348574655812021673416820 1606938044258993025298168039091870024816274313390790265250000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 905 1045463 1073676665 1099510829583 1125899921938025 1152921506180908583 1180591620791358487385 1208925819617312296962463 1237940039285462557626787145 1267650600228231570671872965623

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.4227025.2.
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.eq_ijb$2$(not in LMFDB)