Properties

Label 2.181.abv_bjb
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:  $1 - 47 x + 911 x^{2} - 8507 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.110478730961$, $\pm0.201428511501$
Angle rank:  $2$ (numerical)
Number field:  4.0.398333.1
Galois group:  $D_{4}$
Jacobians:  21

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 21 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25119 1060700013 35156541071331 1151981523639451413 37738796109746922216144 1236354706123826855248022733 40504200058083389457018434821299 1326958065099398815898081038627924197 43472473123840719694418615864712918812559 1424201691976282450216379446367490346577303808

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 135 32375 5928849 1073324923 194265270630 35161843537343 6364291092502401 1151936659092513139 208500535070898045471 37738596846935232325190

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.398333.1.
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.bv_bjb$2$(not in LMFDB)