Properties

Label 2.181.abu_bht
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:  $1 - 46 x + 877 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0353322619336$, $\pm0.246093822352$
Angle rank:  $2$ (numerical)
Number field:  4.0.9837632.1
Galois group:  $D_{4}$
Jacobians:  14

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 14 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25267 1061491937 35154187422508 1151943389876167625 37738579591133669710627 1236353874090791723012253200 40504197628254111986516581601467 1326958059616576061891351181676903625 43472473114871192406284008493876187586828 1424201691968740311181374265944185497218548337

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 136 32400 5928454 1073289396 194264156076 35161819874382 6364290710711356 1151936654332856676 208500535027878840334 37738596846735380193280

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.9837632.1.
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.bu_bht$2$(not in LMFDB)