Properties

Label 2.173.abt_bgn
Base field $\F_{173}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{173}$
Dimension:  $2$
L-polynomial:  $1 - 45 x + 845 x^{2} - 7785 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0929373847626$, $\pm0.228622914131$
Angle rank:  $2$ (numerical)
Number field:  4.0.14449221.1
Galois group:  $D_{4}$
Jacobians:  $40$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $22945$ $885791725$ $26806659400885$ $802389850119073125$ $24013904224903563739600$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $129$ $29595$ $5177313$ $895779283$ $154964513994$ $26808759257235$ $4637914346264853$ $802359178177642243$ $138808137873705675309$ $24013807852720433431350$

Jacobians and polarizations

This isogeny class contains the Jacobians of 40 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{173}$.

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.14449221.1.

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_bgn$2$(not in LMFDB)