//(1/2)(p+1)(p-1+gcd(p-1,3)) algebras
<a,b|pa-bab-xbaaaa,pb-baaa-ybaaaa,class=5>(all x,y, x~-x, y~y' if y^3=y'^3 mod p)(p=1 mod 3)
<a,b|pa-bab-xbaaaa,pb-wbaaa-ybaaaa,class=5>(all x,y, x~-x, y~y' if y^3=y'^3 mod p)(p=1 mod 3)
<a,b|pa-bab-xbaaaa,pb-w^2baaa-ybaaaa,class=5>(all x,y, x~-x, y~y' if y^3=y'^3 mod p)(p=1 mod 3)
<a,b|pa-bab-xbaaaa,pb-baaa-ybaaaa,class=5>(all x,y, x~-x)(p=2 mod 3)
