Properties

Label 2.181.abu_big
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:  $( 1 - 24 x + 181 x^{2} )( 1 - 22 x + 181 x^{2} )$
Frobenius angles:  $\pm0.149335043618$, $\pm0.195291079027$
Angle rank:  $2$ (numerical)
Jacobians:  16

This isogeny class is not 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
$A(\F_{q^r})$ 25280 1062366720 35164839608000 1152012181462548480 37738887442719518072000 1236354924008902610674368000 40504200423153218791646906313920 1326958065180953474933285423842590720 43472473121306251036973743057296846008000 1424201691962858953079224344530585279709888000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 136 32426 5930248 1073353486 194265740776 35161849733978 6364291149864616 1151936659163311006 208500535058742351688 37738596846579535551626

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The isogeny class factors as 1.181.ay $\times$ 1.181.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ac_agk$2$(not in LMFDB)
2.181.c_agk$2$(not in LMFDB)
2.181.bu_big$2$(not in LMFDB)