Properties

Label 2.181.abu_bif
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:  $1 - 46 x + 889 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.138104016676$, $\pm0.203647065452$
Angle rank:  $2$ (numerical)
Number field:  4.0.2113088.3
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25279 1062299417 35164020177244 1152006915524373593 37738864297972275963559 1236354849040065438698824208 40504200251368451931585365622511 1326958065001235253554949631092780713 43472473121972013554405453659494180131836 1424201691967841713947533288547230187767522457

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 136 32424 5930110 1073348580 194265621636 35161847601870 6364291122872644 1151936659007297028 208500535061935449094 37738596846711569100424

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.2113088.3.
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_bif$2$(not in LMFDB)