Properties

Label 2.163.abw_biq
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:  $1 - 48 x + 900 x^{2} - 7824 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0308818759184$, $\pm0.154480826596$
Angle rank:  $2$ (numerical)
Number field:  4.0.55552.1
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 19598 692632516 18736047682094 498290274138211216 13239625854229675403198 351763910495670195532738372 9346014804501584527563610313534 248314265656765545408547646052569088 6597461723335877104962330886684919111918 175287960537011513629511765257251771310835716

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 116 26066 4326284 705881814 115063529156 18755370777026 3057125262158300 498311414352315358 81224760528362714708 13239635966855815968146

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.55552.1.
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.bw_biq$2$(not in LMFDB)