# Properties

 Label 2.181.aby_blz 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: $( 1 - 25 x + 181 x^{2} )^{2}$ Frobenius angles: $\pm0.120568372405$, $\pm0.120568372405$ Angle rank: $1$ (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:

• $y^2=2x^6+2x^3+63$
• $y^2=29x^6+136x^5+143x^4+8x^3+62x^2+167x+49$
• $y^2=78x^6+112x^5+8x^4+17x^3+90x^2+57x+66$
• $y^2=67x^6+65x^5+58x^4+115x^3+19x^2+25x+1$
• $y^2=2x^6+2x^3+98$
• $y^2=155x^6+167x^5+180x^4+170x^3+143x^2+56x+151$
• $y^2=40x^6+30x^5+121x^4+106x^3+177x^2+157x+22$
• $y^2=113x^6+111x^5+83x^4+57x^3+83x^2+111x+113$
• $y^2=7x^6+80x^5+48x^4+160x^3+170x^2+92x+119$
• $y^2=180x^6+128x^5+100x^4+73x^3+80x^2+24x+27$
• $y^2=153x^6+27x^5+15x^4+133x^3+82x^2+177x+41$
• $y^2=2x^6+40x^3+72$
• $y^2=60x^6+12x^5+84x^4+31x^3+104x^2+78x+43$
• $y^2=35x^6+106x^5+161x^4+157x^3+75x^2+177x+20$
• $y^2=107x^6+10x^5+82x^4+56x^3+36x^2+118x+74$
• $y^2=66x^6+131x^5+83x^4+179x^3+123x^2+129x+69$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 24649 1056185001 35137532446864 1151928831456275625 37738705586833646899729 1236354709770217963261956096 40504200797827919818896803132569 1326958068552350574450152154977375625 43472473134445293526388455657638204941584 1424201692000467951679894329279996876751092441

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 132 32236 5925642 1073275828 194264804652 35161843641046 6364291208736012 1151936662090031908 208500535121759180322 37738596847576101448156

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The isogeny class factors as 1.181.az 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-11})$$$)$
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_akd $2$ (not in LMFDB) 2.181.by_blz $2$ (not in LMFDB) 2.181.z_rc $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.181.a_akd $2$ (not in LMFDB) 2.181.by_blz $2$ (not in LMFDB) 2.181.z_rc $3$ (not in LMFDB) 2.181.a_kd $4$ (not in LMFDB) 2.181.az_rc $6$ (not in LMFDB)