Properties

Label 2.163.abs_beu
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:  $1 - 44 x + 800 x^{2} - 7172 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0544015131199$, $\pm0.235892031164$
Angle rank:  $2$ (numerical)
Number field:  4.0.8966400.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20154 697046244 18750605251914 498319254842977296 13239650694675594215514 351763846434730614714341796 9346014462173258990602600942314 248314264837753790602568041152528384 6597461722378049233674707942468928393786 175287960538274245172496395495092430197553124

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 120 26234 4329648 705922870 115063745040 18755367361418 3057125150181096 498311412708741214 81224760516570400824 13239635966951191063514

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.8966400.1.
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_beu$2$(not in LMFDB)