Properties

Label 2.163.abv_bhs
Base Field $\F_{163}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{163}$
Dimension:  $2$
L-polynomial:  $( 1 - 25 x + 163 x^{2} )( 1 - 22 x + 163 x^{2} )$
Frobenius angles:  $\pm0.0652307277549$, $\pm0.169471200781$
Angle rank:  $2$ (numerical)
Jacobians:  6

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 contains the Jacobians of 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 19738 693869652 18741129704584 498305704588028064 13239664678055109160198 351763995867747776897927616 9346014976339352433214833392566 248314265995952852723102043008476800 6597461724061444237479894470714188442536 175287960538814079750701002976819841202234452

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 117 26113 4327458 705903673 115063866567 18755375328898 3057125318367237 498311415032988721 81224760537295546614 13239635966991965188993

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The isogeny class factors as 1.163.az $\times$ 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.163.ad_aiq$2$(not in LMFDB)
2.163.d_aiq$2$(not in LMFDB)
2.163.bv_bhs$2$(not in LMFDB)
2.163.ao_fu$3$(not in LMFDB)
2.163.af_abw$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.163.ad_aiq$2$(not in LMFDB)
2.163.d_aiq$2$(not in LMFDB)
2.163.bv_bhs$2$(not in LMFDB)
2.163.ao_fu$3$(not in LMFDB)
2.163.af_abw$3$(not in LMFDB)
2.163.abn_bay$6$(not in LMFDB)
2.163.abe_ti$6$(not in LMFDB)
2.163.f_abw$6$(not in LMFDB)
2.163.o_fu$6$(not in LMFDB)
2.163.be_ti$6$(not in LMFDB)
2.163.bn_bay$6$(not in LMFDB)