Properties

Label 2.163.abu_bgv
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:  $1 - 46 x + 853 x^{2} - 7498 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0946297427759$, $\pm0.179383193902$
Angle rank:  $2$ (numerical)
Number field:  4.0.666176.1
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
$A(\F_{q^r})$ 19879 695108993 18746213076100 498321129823562249 13239703393800730092079 351764080142640759472499600 9346015140319853725165280767831 248314266290596779537866711079097289 6597461724574707060254092702599905808100 175287960539734681947521569950486895658203953

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 118 26160 4328632 705925524 115064203038 18755379822270 3057125372006026 498311415624273444 81224760543614590456 13239635967061498988800

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.666176.1.
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.bu_bgv$2$(not in LMFDB)