Properties

Label 2.163.abt_bfy
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:  $( 1 - 24 x + 163 x^{2} )( 1 - 21 x + 163 x^{2} )$
Frobenius angles:  $\pm0.110906256499$, $\pm0.192621479609$
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
$A(\F_{q^r})$ 20020 696295600 18750698926960 498332981666520000 13239726812928470955100 351764112081552209213574400 9346015153504920139526171434540 248314266209272410505346187719520000 6597461724265388518104214653341529869680 175287960539065283354412669708618874452190000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 119 26205 4329668 705942313 115064406569 18755381525190 3057125376318923 498311415461073553 81224760539806410044 13239635967010938792525

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The isogeny class factors as 1.163.ay $\times$ 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 is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.163.ad_agw$2$(not in LMFDB)
2.163.d_agw$2$(not in LMFDB)
2.163.bt_bfy$2$(not in LMFDB)