Properties

Label 2.163.abr_beb
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:  $1 - 43 x + 781 x^{2} - 7009 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.103645999267$, $\pm0.236451097903$
Angle rank:  $2$ (numerical)
Number field:  4.0.16736741.1
Galois group:  $D_{4}$
Jacobians:  18

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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20299 698346497 18756303423949 498338438000287469 13239706046996518355824 351763989737118496904698241 9346014802114919845139972689177 248314265581212192588697788499265525 6597461723866286686473975209234896401991 175287960540929659128520657845331432652228352

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 121 26283 4330963 705950043 115064226096 18755375002023 3057125261377609 498311414200696611 81224760534892861159 13239635967151756544518

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.16736741.1.
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.br_beb$2$(not in LMFDB)