Properties

Label 2.163.abt_bga
Base Field $\F_{163}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{163}$
Dimension:  $2$
L-polynomial:  $( 1 - 23 x + 163 x^{2} )( 1 - 22 x + 163 x^{2} )$
Frobenius angles:  $\pm0.143017980409$, $\pm0.169471200781$
Angle rank:  $2$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20022 696405204 18751870232424 498339725245423776 13239754048664089849482 351764196805367954013422016 9346015360336874235058179532698 248314266580324706048269890073355904 6597461724573530152385565850211217707016 175287960538074179221882105868104092499808724

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 119 26209 4329938 705951865 115064643269 18755386042498 3057125443974623 498311416205692849 81224760543600100934 13239635966936079926689

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The isogeny class factors as 1.163.ax $\times$ 1.163.aw 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 $\F_{163}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.163.ab_agy$2$(not in LMFDB)
2.163.b_agy$2$(not in LMFDB)
2.163.bt_bga$2$(not in LMFDB)