Properties

Label 2.173.abu_bho
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:  $1 - 46 x + 872 x^{2} - 7958 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.110664567545$, $\pm0.200287313354$
Angle rank:  $2$ (numerical)
Number field:  4.0.2772288.1
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
$A(\F_{q^r})$ 22798 884699188 26804235111838 802393063990308304 24013950198826443390238 718709615709723743121433876 21510249970813891935247398302734 643780252175911282890694904028484608 19267699141312513398931957407016192553182 576662967581705708988630443182184551067533588

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 128 29558 5176844 895782870 154964810668 26808766778774 4637914471195504 802359179586669790 138808137880750303376 24013807852593727958438

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.2772288.1.
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.bu_bho$2$(not in LMFDB)