Properties

Label 2.163.abs_bfd
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:  $( 1 - 23 x + 163 x^{2} )( 1 - 21 x + 163 x^{2} )$
Frobenius angles:  $\pm0.143017980409$, $\pm0.192621479609$
Angle rank:  $2$ (numerical)
Jacobians:  18

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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20163 697538985 18755758417968 498348012083632425 13239762329938211361723 351764177975644244923157760 9346015233576500732290039838979 248314266182037699972042457393161225 6597461723708959919345362999040193928752 175287960536858539324477701783840826443706425

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 120 26252 4330836 705963604 115064715240 18755385038534 3057125402510712 498311415406419556 81224760532955930028 13239635966844261699932

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The isogeny class factors as 1.163.ax $\times$ 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.ac_agb$2$(not in LMFDB)
2.163.c_agb$2$(not in LMFDB)
2.163.bs_bfd$2$(not in LMFDB)