# Properties

 Label 2.181.abu_big Base Field $\F_{181}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## 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:

• $y^2=74x^6+72x^5+102x^4+59x^3+101x^2+85x+146$
• $y^2=51x^6+160x^5+75x^4+64x^3+75x^2+160x+51$
• $y^2=63x^6+3x^5+22x^4+171x^3+120x^2+x+131$
• $y^2=19x^6+39x^5+95x^4+53x^3+95x^2+39x+19$
• $y^2=71x^6+125x^5+56x^4+24x^3+178x^2+16x+159$
• $y^2=126x^6+135x^5+93x^4+163x^3+71x^2+177x+116$
• $y^2=77x^6+125x^5+63x^4+58x^3+98x^2+117x+157$
• $y^2=88x^6+165x^5+113x^4+16x^3+113x^2+165x+88$
• $y^2=40x^6+73x^5+94x^4+43x^3+20x^2+75x+51$
• $y^2=146x^6+15x^5+92x^4+29x^3+92x^2+15x+146$
• $y^2=112x^6+50x^5+146x^4+18x^3+146x^2+50x+112$
• $y^2=179x^6+179x^5+8x^4+98x^3+107x^2+123x+84$
• $y^2=26x^6+55x^4+5x^3+55x^2+26$
• $y^2=102x^6+78x^5+44x^4+43x^3+44x^2+78x+102$
• $y^2=164x^6+119x^5+7x^4+23x^3+92x^2+180x+109$
• $y^2=4x^6+85x^5+22x^4+95x^3+22x^2+85x+4$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 25280 1062366720 35164839608000 1152012181462548480 37738887442719518072000 1236354924008902610674368000 40504200423153218791646906313920 1326958065180953474933285423842590720 43472473121306251036973743057296846008000 1424201691962858953079224344530585279709888000

 $r$ 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.
 Twist Extension Degree Common 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)