Properties

Label 2.173.abv_bio
Base Field $\F_{173}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{173}$
Dimension:  $2$
L-polynomial:  $( 1 - 24 x + 173 x^{2} )( 1 - 23 x + 173 x^{2} )$
Frobenius angles:  $\pm0.134271185755$, $\pm0.161302001611$
Angle rank:  $2$ (numerical)
Jacobians:  0

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 is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22650 883485900 26800490008800 802389032946072000 24013970554885867223250 718709758864758143080646400 21510250500426649639749763928850 643780253562920817760338094334304000 19267699143792078937748143503941153522400 576662967583061610311515019121461366460619500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 127 29517 5176120 895778369 154964942027 26808772118634 4637914585387511 802359181315333921 138808137898613561080 24013807852650191361957

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.ay $\times$ 1.173.ax 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 $\F_{173}$.

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.ab_ahy$2$(not in LMFDB)
2.173.b_ahy$2$(not in LMFDB)
2.173.bv_bio$2$(not in LMFDB)