Properties

Label 2.173.abu_bhr
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:  $( 1 - 23 x + 173 x^{2} )^{2}$
Frobenius angles:  $\pm0.161302001611$, $\pm0.161302001611$
Angle rank:  $1$ (numerical)
Jacobians:  7

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 contains the Jacobians of 7 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22801 884884009 26806381990144 802406420764930921 24014008152537131333641 718709807617138222971621376 21510250460394996583407142930081 643780253043866322366654638191305609 19267699141692080490441191421122782279936 576662967576944433891806754651600326709227449

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 128 29564 5177258 895797780 154965184648 26808773937158 4637914576756120 802359180668423524 138808137883484776274 24013807852395455567564

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.ax 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-163}) \)$)$
All geometric endomorphisms are defined over $\F_{173}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.a_ahb$2$(not in LMFDB)
2.173.bu_bhr$2$(not in LMFDB)
2.173.x_ns$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.a_ahb$2$(not in LMFDB)
2.173.bu_bhr$2$(not in LMFDB)
2.173.x_ns$3$(not in LMFDB)
2.173.a_hb$4$(not in LMFDB)
2.173.ax_ns$6$(not in LMFDB)