Properties

Label 2.173.abt_bgl
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:  $1 - 45 x + 843 x^{2} - 7785 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0769286473055$, $\pm0.234964715490$
Angle rank:  $2$ (numerical)
Number field:  4.0.17004349.1
Galois group:  $D_{4}$
Jacobians:  17

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 17 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22943 885668629 26805259424531 802381386475467301 24013868660564699460368 718709299416601033414918261 21510249098252171299024335866027 643780250458724369482787787340984389 19267699139501291779292752896543037478519 576662967584304721262091998695377765194093824

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 129 29591 5177043 895769835 154964284494 26808754980647 4637914283058843 802359177446497459 138808137867701921289 24013807852701957868886

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.17004349.1.
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_bgl$2$(not in LMFDB)