Properties

Label 2.181.abv_bix
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:  $1 - 47 x + 907 x^{2} - 8507 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0735271811030$, $\pm0.218603882480$
Angle rank:  $2$ (numerical)
Number field:  4.0.9288845.1
Galois group:  $D_{4}$
Jacobians:  26

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 26 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25115 1060430645 35153191972535 1151959197600393125 37738691657319842226000 1236354327289656845189542805 40504198956625252377533167573535 1326958062572096124721435123170093125 43472473119770493509724496691674201505315 1424201691974703652776052342855632923666208000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 135 32367 5928285 1073304123 194264732950 35161832763327 6364290919433925 1151936656898553363 208500535051376627055 37738596846893397239302

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.9288845.1.
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.bv_bix$2$(not in LMFDB)