Properties

Label 2.163.abr_bea
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:  $1 - 43 x + 780 x^{2} - 7009 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0963982022717$, $\pm0.239744545163$
Angle rank:  $2$ (numerical)
Number field:  4.0.19262232.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20298 698291796 18755743913784 498335420686303776 13239694889809631911398 351763958818569339281564352 9346014737384744374021949897334 248314265488891582784136171878855808 6597461723833054166967448120499057624088 175287960541223469120983735452626244733879316

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 121 26281 4330834 705945769 115064129131 18755373353506 3057125240204065 498311414015429713 81224760534483718438 13239635967173948241721

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.19262232.1.
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_bea$2$(not in LMFDB)