Properties

Label 2.163.abu_bgr
Base Field $\F_{163}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{163}$
Dimension:  $2$
L-polynomial:  $1 - 46 x + 849 x^{2} - 7498 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0259491891705$, $\pm0.202261752526$
Angle rank:  $2$ (numerical)
Number field:  4.0.571968.5
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
$A(\F_{q^r})$ 19875 694889625 18743818270500 498306840625745625 13239642313044741961875 351763871842138011168474000 9346014544332082720784570524875 248314264825521691677280610111075625 6597461721457477517793056403453748426500 175287960534032556327597431329248589783685625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 118 26152 4328080 705905284 115063672198 18755368716094 3057125177055634 498311412684194116 81224760505236766720 13239635966630813006632

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.571968.5.
All geometric endomorphisms are defined over $\F_{163}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.163.bu_bgr$2$(not in LMFDB)