Properties

Label 2.173.abt_bgp
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:  $1 - 45 x + 847 x^{2} - 7785 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.108541149926$, $\pm0.221142714353$
Angle rank:  $2$ (numerical)
Number field:  4.0.9679509.2
Galois group:  $D_{4}$
Jacobians:  28

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 28 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22947 885914829 26808059397519 802398299452863381 24013939510321981217232 718709525895262422149398701 21510249664811714400329303002863 643780251525355113091705275540554469 19267699140696531753532464600346948317411 576662967583435189927753340573121418991188224

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 129 29599 5177583 895788715 154964741694 26808763428583 4637914405217103 802359178775865619 138808137876312655449 24013807852665748229014

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.9679509.2.
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.bt_bgp$2$(not in LMFDB)