Properties

Label 2.173.abu_bhh
Base Field $\F_{173}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{173}$
Dimension:  $2$
L-polynomial:  $1 - 46 x + 865 x^{2} - 7958 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0332764210250$, $\pm0.228065115178$
Angle rank:  $2$ (numerical)
Number field:  4.0.3598400.2
Galois group:  $D_{4}$
Jacobians:  10

This isogeny class is simple and geometrically simple.

Newton polygon

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

Point counts

This isogeny class contains the Jacobians of 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22791 884268009 26799225911964 802361772986057721 24013812478727173114191 718709141991039515577136656 21510248641020317590482971119911 643780249097012098748071480888155369 19267699135550607373564381455713949905916 576662967573654117899237464979954793487283049

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 128 29544 5175878 895747940 154963921948 26808749108478 4637914184473180 802359175749361924 138808137839240445854 24013807852258437897864

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.3598400.2.
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.bu_bhh$2$(not in LMFDB)