# Properties

 Label 2.181.abv_bjc 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: $( 1 - 25 x + 181 x^{2} )( 1 - 22 x + 181 x^{2} )$ Frobenius angles: $\pm0.120568372405$, $\pm0.195291079027$ Angle rank: $2$ (numerical) Jacobians: 24

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 24 curves, and hence is principally polarizable:

• $y^2=95x^6+174x^5+158x^4+39x^3+11x^2+78x+84$
• $y^2=83x^6+137x^5+23x^4+130x^3+51x^2+153x+165$
• $y^2=66x^6+42x^5+180x^4+89x^3+164x^2+162x+140$
• $y^2=11x^6+162x^5+115x^4+83x^3+129x^2+103x+67$
• $y^2=6x^6+119x^5+132x^4+163x^3+128x^2+86x+131$
• $y^2=63x^6+170x^5+33x^4+81x^3+141x^2+176x+179$
• $y^2=39x^6+140x^5+54x^4+21x^3+172x^2+58x+166$
• $y^2=74x^6+109x^5+112x^4+147x^3+52x^2+153x+147$
• $y^2=89x^6+130x^5+152x^4+90x^3+64x^2+90x+150$
• $y^2=19x^6+86x^5+133x^4+170x^3+13x^2+173x+72$
• $y^2=18x^6+69x^5+78x^4+77x^3+20x^2+76x+134$
• $y^2=154x^6+173x^5+33x^4+178x^3+70x^2+18x+76$
• $y^2=110x^6+176x^5+42x^4+9x^3+66x^2+135x+86$
• $y^2=126x^6+121x^5+96x^4+75x^3+88x^2+161x+57$
• $y^2=107x^6+48x^5+31x^4+170x^3+19x^2+35x+154$
• $y^2=81x^6+165x^5+45x^4+43x^3+146x^2+31x+169$
• $y^2=112x^6+116x^5+147x^4+12x^3+41x^2+22x+88$
• $y^2=175x^6+19x^5+76x^4+146x^3+106x^2+124x+151$
• $y^2=174x^6+79x^5+53x^4+118x^3+27x^2+11x+159$
• $y^2=19x^6+114x^5+102x^4+143x^3+62x^2+157x+71$
• $y^2=89x^6+111x^5+152x^4+112x^3+23x^2+86x+33$
• $y^2=94x^6+163x^5+101x^4+14x^3+121x^2+27x+174$
• $y^2=63x^6+15x^5+155x^4+85x^3+47x^2+118x+6$
• $y^2=41x^6+115x^5+140x^4+176x^3+140x^2+144x+47$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 25120 1060767360 35157378359680 1151987094432576000 37738821994604977348000 1236354798297031772995952640 40504200313880881812351672722080 1326958065613867935854030242288896000 43472473124279575131677789025002677467520 1424201691974259127235077150178790576090384000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 135 32377 5928990 1073330113 194265403875 35161846158742 6364291132695015 1151936659539125473 208500535073002862310 37738596846881618170177

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The isogeny class factors as 1.181.az $\times$ 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.ad_ahg $2$ (not in LMFDB) 2.181.d_ahg $2$ (not in LMFDB) 2.181.bv_bjc $2$ (not in LMFDB)