Properties

Label 2.173.abu_bhm
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:  $1 - 46 x + 870 x^{2} - 7958 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0910915092874$, $\pm0.210430033938$
Angle rank:  $2$ (numerical)
Number field:  4.0.359600.1
Galois group:  $D_{4}$
Jacobians:  36

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 36 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22796 884575984 26802803885804 802384141588810496 24013911206623264875916 718709484069168995697852016 21510249617724350393095064281196 643780251447829048075128556757233664 19267699140373620302461417056164050518476 576662967582225629811849539454304474219648624

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 128 29554 5176568 895772910 154964559048 26808761868418 4637914395064400 802359178679242974 138808137873986340464 24013807852615378869714

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.359600.1.
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_bhm$2$(not in LMFDB)