Properties

Label 2.173.abv_bil
Base Field $\F_{173}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{173}$
Dimension:  $2$
L-polynomial:  $1 - 47 x + 895 x^{2} - 8131 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0881869395452$, $\pm0.191285016768$
Angle rank:  $2$ (numerical)
Number field:  4.0.1935557.1
Galois group:  $D_{4}$
Jacobians:  18

This isogeny class is simple and geometrically 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
$A(\F_{q^r})$ 22647 883300941 26798296309443 802374923595026421 24013906206530330034192 718709528842278431312091357 21510249833146758795490279296867 643780252013139864891546365931978213 19267699141213841933977291950633403696551 576662967581889765667151030412422145898434816

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 127 29511 5175697 895762619 154964526782 26808763538511 4637914441512521 802359179383803763 138808137880039455535 24013807852601392577046

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.1935557.1.
All geometric endomorphisms are defined over $\F_{173}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.bv_bil$2$(not in LMFDB)