Properties

Label 2.173.abt_bgt
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:  $1 - 45 x + 851 x^{2} - 7785 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.145147992759$, $\pm0.197931037552$
Angle rank:  $2$ (numerical)
Number field:  4.0.9725.1
Galois group:  $D_{4}$
Jacobians:  11

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 11 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22951 886161061 26810859451819 802415155191647301 24014009244398486526736 718709741098833094953484741 21510250152737470377349487338099 643780252169331081731241422060830725 19267699140043949690533159641708754640431 576662967575822477101678566181072335384560896

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 129 29607 5178123 895807531 154965191694 26808771455943 4637914510420803 802359179578468723 138808137871611331209 24013807852348734248022

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.9725.1.
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.bt_bgt$2$(not in LMFDB)