Properties

Label 2.173.abu_bhl
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:  $1 - 46 x + 869 x^{2} - 7958 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0814447409702$, $\pm0.214601179315$
Angle rank:  $2$ (numerical)
Number field:  4.0.6884928.2
Galois group:  $D_{4}$
Jacobians:  14

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 14 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22795 884514385 26802088280620 802379675022474025 24013891603602758580475 718709417137242875727596560 21510249433142056662099751928995 643780251038565996840205091571436425 19267699139694550249337142266201659392460 576662967581659487556949296418471603368923425

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 128 29552 5176430 895767924 154964432548 26808759371774 4637914355265844 802359178169168356 138808137869094191750 24013807852591803172832

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.6884928.2.
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.bu_bhl$2$(not in LMFDB)