Properties

Label 2.163.abs_bfb
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:  $1 - 44 x + 807 x^{2} - 7172 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.120308870982$, $\pm0.208123667354$
Angle rank:  $2$ (numerical)
Number field:  4.0.3084048.5
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20161 697429473 18754613236132 498341641315918569 13239737876475551224201 351764107606222239160052496 9346015083495737380582525381153 248314265989821398319274099337622153 6597461723847445298232887206350635674756 175287960538660196720852373697576524415955313

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 120 26248 4330572 705954580 115064502720 18755381286574 3057125353418592 498311415020684260 81224760534660895092 13239635966980342284088

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.3084048.5.
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.bs_bfb$2$(not in LMFDB)