Properties

Label 2.173.abv_bik
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:  $1 - 47 x + 894 x^{2} - 8131 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0759020846038$, $\pm0.196754742414$
Angle rank:  $2$ (numerical)
Number field:  4.0.2592908.1
Galois group:  $D_{4}$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22646 883239292 26797565087072 802370213324710784 24013884611421665663326 718709450612465015369106688 21510249599099075499993220238222 643780251428559875789181327322414592 19267699140024355595300844196387736546912 576662967580125011422975868897681781085489372

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 127 29509 5175556 895757361 154964387427 26808760620442 4637914391048527 802359178655227329 138808137871470171652 24013807852527903430509

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.2592908.1.
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.bv_bik$2$(not in LMFDB)