Properties

Label 2.181.abx_bkx
Base Field $\F_{181}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{181}$
Dimension:  $2$
L-polynomial:  $1 - 49 x + 959 x^{2} - 8869 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0675982025699$, $\pm0.180470077574$
Angle rank:  $2$ (numerical)
Number field:  4.0.1135173.1
Galois group:  $D_{4}$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24803 1057575117 35142370370207 1151935362697290453 37738676653843304208848 1236354452391478605162859053 40504199608056186689785443397103 1326958064388154862209487292480063333 43472473122550704469494311585523026472083 1424201691972766514473158991316868880084760832

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 133 32279 5926459 1073281915 194264655718 35161836321215 6364291021791115 1151936658475079923 208500535064710937965 37738596846842066811974

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.1135173.1.
All geometric endomorphisms are defined over $\F_{181}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.181.bx_bkx$2$(not in LMFDB)