Properties

Label 2.173.abu_bhj
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:  $1 - 46 x + 867 x^{2} - 7958 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0607391626202$, $\pm0.221843767921$
Angle rank:  $2$ (numerical)
Number field:  4.0.454208.1
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
$A(\F_{q^r})$ 22793 884391193 26800657085888 802370731158521609 24013852183723744503313 718709281048484448759479296 21510249047857620904954930510409 643780250128948522790323408161886793 19267699137910701017586591038662981518272 576662967578825036520052038599498125911493513

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 128 29548 5176154 895757940 154964178168 26808754295494 4637914272193064 802359177035489700 138808137856243005506 24013807852473768954588

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.454208.1.
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_bhj$2$(not in LMFDB)