Properties

Label 2.163.abs_bew
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:  $1 - 44 x + 802 x^{2} - 7172 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0750186375807$, $\pm0.229660133188$
Angle rank:  $2$ (numerical)
Number field:  4.0.161792.1
Galois group:  $D_{4}$
Jacobians:  28

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 28 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20156 697155728 18751750366172 498325665071335424 13239675856885541673276 351763923419451839435862416 9346014655004292683495701109468 248314265243853003677588645263474688 6597461723115701991549958461823964276156 175287960539499484493977236503820760258297488

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 120 26238 4329912 705931950 115063963720 18755371466094 3057125213257032 498311413523691870 81224760525652025112 13239635967043734342238

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.161792.1.
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_bew$2$(not in LMFDB)