Properties

Label 2.163.abu_bgt
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:  $( 1 - 25 x + 163 x^{2} )( 1 - 21 x + 163 x^{2} )$
Frobenius angles:  $\pm0.0652307277549$, $\pm0.192621479609$
Angle rank:  $2$ (numerical)
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 19877 694999305 18745015663088 498313990860510825 13239672959273330652797 351763977038034823876373760 9346014849578984138620167745493 248314265597665847584185700429535625 6597461723196874004506798373211405278192 175287960537598439853291467606869972049864025

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 118 26156 4328356 705915412 115063938538 18755374324934 3057125276903326 498311414233715428 81224760526651375708 13239635966900146962236

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The isogeny class factors as 1.163.az $\times$ 1.163.av 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.ae_ahr$2$(not in LMFDB)
2.163.e_ahr$2$(not in LMFDB)
2.163.bu_bgt$2$(not in LMFDB)
2.163.an_gc$3$(not in LMFDB)
2.163.ae_abf$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.163.ae_ahr$2$(not in LMFDB)
2.163.e_ahr$2$(not in LMFDB)
2.163.bu_bgt$2$(not in LMFDB)
2.163.an_gc$3$(not in LMFDB)
2.163.ae_abf$3$(not in LMFDB)
2.163.abm_bah$6$(not in LMFDB)
2.163.abd_ta$6$(not in LMFDB)
2.163.e_abf$6$(not in LMFDB)
2.163.n_gc$6$(not in LMFDB)
2.163.bd_ta$6$(not in LMFDB)
2.163.bm_bah$6$(not in LMFDB)