Properties

Label 2.181.abw_bjv
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:  $1 - 48 x + 931 x^{2} - 8688 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0444136033573$, $\pm0.208191558910$
Angle rank:  $2$ (numerical)
Number field:  4.0.326928.1
Galois group:  $D_{4}$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24957 1058900553 35146462028868 1151937843870675033 37738635441619717040157 1236354187746056142843379728 40504198573342658378330641724373 1326958061323174420833762622576577577 43472473115411293815173262518229776350308 1424201691960315263153830543224029696807639433

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 134 32320 5927150 1073284228 194264443574 35161828794718 6364290859209998 1151936655814360324 208500535030469248118 37738596846512132676640

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.326928.1.
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.bw_bjv$2$(not in LMFDB)