Properties

Label 2.163.abt_bfz
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:  $1 - 45 x + 831 x^{2} - 7335 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.124103562334$, $\pm0.184084818071$
Angle rank:  $2$ (numerical)
Number field:  4.0.458725.1
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
$A(\F_{q^r})$ 20021 696350401 18751284577199 498336354865078621 13239740456683763216336 351764154691761536124755881 9346015258577247312135231101819 248314266403387095924904958631868725 6597461724456035639264847573343393464761 175287960538701281455212628464234749067364096

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 119 26207 4329803 705947091 115064525144 18755383797083 3057125410688573 498311415850618483 81224760542153565269 13239635966983445446022

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.458725.1.
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.bt_bfz$2$(not in LMFDB)