Properties

Label 2.1024.aep_ige
Base Field $\F_{2^{10}}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{10}}$
Dimension:  $2$
L-polynomial:  $( 1 - 32 x )^{2}( 1 - 55 x + 1024 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.170852887823$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

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
$A(\F_{q^r})$ 932170 1096343780400 1152853913463294490 1208924770098697393500000 1267650592446413907299277375850 1329227995777211789711192531945523600 1393796574893268000546984411502451776186810 1461501637329324559982619867313794171301971000000 1532495540865791459292929135192228270552006218300619530 1606938044258985681949005821574657304299783129639078675510000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 906 1045552 1073678874 1099510673248 1125899899930986 1152921504600164752 1180591620704793946554 1208925819613323587386048 1237940039285301596560653066 1267650600228225777790805504752

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The isogeny class factors as 1.1024.acm $\times$ 1.1024.acd and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{10}}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.1024.aj_aceq$2$(not in LMFDB)
2.1024.j_aceq$2$(not in LMFDB)
2.1024.ep_ige$2$(not in LMFDB)
2.1024.ax_lc$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.1024.aj_aceq$2$(not in LMFDB)
2.1024.j_aceq$2$(not in LMFDB)
2.1024.ep_ige$2$(not in LMFDB)
2.1024.ax_lc$3$(not in LMFDB)
2.1024.acd_dau$4$(not in LMFDB)
2.1024.cd_dau$4$(not in LMFDB)
2.1024.adj_fqm$6$(not in LMFDB)
2.1024.x_lc$6$(not in LMFDB)
2.1024.dj_fqm$6$(not in LMFDB)