Properties

Label 2.173.abv_bih
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:  $1 - 47 x + 891 x^{2} - 8131 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0295549099493$, $\pm0.209571521819$
Angle rank:  $2$ (numerical)
Number field:  4.0.1295981.1
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22643 883054357 26795371452119 802356061053561989 24013819389124717592848 718709211251559834988155301 21510248861964692769772726156751 643780249468961074161883329896243525 19267699135446151549326293040681765644411 576662967570552245555985868309193349494609152

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 127 29503 5175133 895741563 154963966542 26808751691983 4637914232111917 802359176212931091 138808137838487926399 24013807852129267532118

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.1295981.1.
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_bih$2$(not in LMFDB)