Properties

Label 2.1024.ai_agd
Base field $\F_{2^{10}}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{2^{10}}$
Dimension:  $2$
L-polynomial:  $1 - 8 x - 159 x^{2} - 8192 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.205257621131$, $\pm0.735510757239$
Angle rank:  $2$ (numerical)
Number field:  4.0.149350032.2
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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $1040218$ $1099113062724$ $1152890470103202106$ $1208930038224502123323648$ $1267650635534099477144686846138$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $1017$ $1048195$ $1073712921$ $1099515464575$ $1125899938200537$ $1152921505631535619$ $1180591620792333810489$ $1208925819611625189972223$ $1237940039285343668795297721$ $1267650600228228170315560289155$

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.149350032.2.
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.i_agd$2$(not in LMFDB)