Properties

Label 2.181.abw_bka
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:  $1 - 48 x + 936 x^{2} - 8688 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.106535498304$, $\pm0.182910012524$
Angle rank:  $2$ (numerical)
Number field:  4.0.1069312.2
Galois group:  $D_{4}$
Jacobians:  20

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 20 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24962 1059237508 35150737767698 1151967265054901008 37738779508651095468482 1236354745527404537608960708 40504200360789927663426453672338 1326958066133391071546049162471800832 43472473126132433411412775336377723382658 1424201691978810094306105712934495158401816708

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 134 32330 5927870 1073311638 194265185174 35161844657978 6364291140065678 1151936659990125214 208500535081889449958 37738596847002210016490

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.1069312.2.
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_bka$2$(not in LMFDB)