Properties

Label 2.163.abv_bht
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:  $1 - 47 x + 877 x^{2} - 7661 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0855301227133$, $\pm0.159842173573$
Angle rank:  $2$ (numerical)
Number field:  4.0.173525.1
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 19739 693924545 18741741484901 498309467549648525 13239681415912501372944 351764055839889423733380305 9346015158396154635379748719841 248314266475167898927031879757569525 6597461725160159923451262826973078849879 175287960540971134491693680969485250854368000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 117 26115 4327599 705909003 115064012032 18755378526495 3057125377918869 498311415994666563 81224760550822403187 13239635967154889210950

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.173525.1.
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.bv_bht$2$(not in LMFDB)