Properties

Label 2.181.abw_bjx
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:  $1 - 48 x + 933 x^{2} - 8688 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0712454186694$, $\pm0.200090328096$
Angle rank:  $2$ (numerical)
Number field:  4.0.223225.1
Galois group:  $D_{4}$
Jacobians:  26

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 26 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24959 1059035329 35148172307600 1151949625203197689 37738693348157251730159 1236354414051843772059193600 40504199313841249184543793568439 1326958063407257852230386150864319209 43472473120534709508328530359127008051600 1424201691971468400425020060344709884846784609

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 134 32324 5927438 1073295204 194264741654 35161835230838 6364290975562094 1151936657623560004 208500535055041922198 37738596846807669294404

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.223225.1.
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.bw_bjx$2$(not in LMFDB)