Properties

Label 2.181.abu_bie
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:  $1 - 46 x + 888 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.128869422289$, $\pm0.209863845130$
Angle rank:  $2$ (numerical)
Number field:  4.0.4394304.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25278 1062232116 35163200751822 1152001645299224016 37738841063867831322798 1236354773107093111210954644 40504200072427524449303773298142 1326958064780810268054416696232612864 43472473122451322928024269368396291994382 1424201691972125116003425143849911453572691476

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 136 32422 5929972 1073343670 194265502036 35161845442342 6364291094756248 1151936658815945374 208500535064234289112 37738596846825070990102

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.4394304.1.
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_bie$2$(not in LMFDB)