Properties

Label 2.181.abu_bhu
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:  $1 - 46 x + 878 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0477114349732$, $\pm0.243779660740$
Angle rank:  $2$ (numerical)
Number field:  4.0.105456.1
Galois group:  $D_{4}$
Jacobians:  48

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 48 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25268 1061559216 35155006789652 1151948707259440896 37738603808169621776948 1236353960657101254022784304 40504197886724331471850431138452 1326958060296989170815982480645484544 43472473116569126049789950620014111350132 1424201691973154638205713010987598553608822576

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 136 32402 5928592 1073294350 194264280736 35161822336322 6364290751323928 1151936654923525534 208500535036022386072 37738596846852351342002

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.105456.1.
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_bhu$2$(not in LMFDB)