Properties

Label 2.163.abu_bgs
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:  $1 - 46 x + 850 x^{2} - 7498 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0486964346780$, $\pm0.197735354640$
Angle rank:  $2$ (numerical)
Number field:  4.0.83600.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 19876 694944464 18744416964244 498310417152102656 13239657662621701104916 351763924701610325593522256 9346014698771740603393140190756 248314265221535860602831836758052864 6597461722372755883485648672745615183876 175287960535997057480030111929678805751622224

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 118 26154 4328218 705910350 115063805598 18755371534458 3057125227573570 498311413478906334 81224760516505231654 13239635966779193306314

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.83600.1.
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_bgs$2$(not in LMFDB)