Properties

Label 2.163.abs_bez
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:  $1 - 44 x + 805 x^{2} - 7172 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.101937801983$, $\pm0.218245318378$
Angle rank:  $2$ (numerical)
Number field:  4.0.422225.1
Galois group:  $D_{4}$
Jacobians:  30

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 30 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20159 697319969 18753468073664 498335259273928121 13239713220513952313439 351764035348965653044576256 9346014921257106926288106394679 248314265737229287625651061316740329 6597461723742160079979377897507574286016 175287960539642206248789684544930545089716449

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 120 26244 4330308 705945540 115064288440 18755377433958 3057125300349576 498311414513788164 81224760533364674364 13239635967054514227364

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.422225.1.
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.bs_bez$2$(not in LMFDB)