# Properties

 Label 2.181.abw_bkc 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: $( 1 - 24 x + 181 x^{2} )^{2}$ Frobenius angles: $\pm0.149335043618$, $\pm0.149335043618$ Angle rank: $1$ (numerical) Jacobians: 13

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 13 curves, and hence is principally polarizable:

• $y^2=81x^6+177x^5+95x^4+75x^3+136x^2+61x+58$
• $y^2=65x^6+9x^5+86x^4+171x^3+63x^2+153x+89$
• $y^2=164x^6+64x^5+7x^4+83x^3+65x^2+34x+6$
• $y^2=139x^6+78x^5+103x^4+43x^3+100x^2+16x+134$
• $y^2=6x^6+78x^5+70x^4+18x^3+70x^2+78x+6$
• $y^2=46x^6+48x^5+5x^4+151x^3+159x^2+171x+121$
• $y^2=158x^6+180x^5+162x^4+73x^3+169x^2+51x+147$
• $y^2=91x^6+46x^5+120x^4+87x^3+120x^2+46x+91$
• $y^2=35x^6+126x^5+154x^4+29x^3+7x^2+50x+32$
• $y^2=122x^6+48x^5+114x^4+164x^3+117x^2+133x+2$
• $y^2=96x^6+112x^5+116x^4+30x^3+93x^2+x+47$
• $y^2=15x^6+114x^4+114x^2+15$
• $y^2=58x^6+50x^5+171x^4+48x^3+168x^2+138x+177$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 24964 1059372304 35152448102500 1151979003524911104 37738836482772472975684 1236354961193954418216490000 40504201016372596683469625079844 1326958067686521650832563947218468864 43472473128498645335793145903627245002500 1424201691977667603367860389237713356249063184

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 134 32334 5928158 1073322574 194265478454 35161850791518 6364291243075214 1151936661338402974 208500535093238159078 37738596846971936211054

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The isogeny class factors as 1.181.ay 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-37})$$$)$
All geometric endomorphisms are defined over $\F_{181}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.181.a_aig $2$ (not in LMFDB) 2.181.bw_bkc $2$ (not in LMFDB) 2.181.y_pf $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.181.a_aig $2$ (not in LMFDB) 2.181.bw_bkc $2$ (not in LMFDB) 2.181.y_pf $3$ (not in LMFDB) 2.181.a_ig $4$ (not in LMFDB) 2.181.ay_pf $6$ (not in LMFDB)