K13a248

Knotscape

Three trefoil knots along a closed loop, mutually interlinked.

Dowker-Thistlethwaite code

4 8 14 2 16 20 6 26 12 24 10 18 22

Jones polynomial	Data:K13a248/Jones Polynomial
Alexander polynomial	$9t^{3}-38t^{2}+79t-99+79t^{-1}-38t^{-2}+9t^{-3}$
Conway polynomial	Data:K13a248/Conway Polynomial
Determinant	351
Signature	6
HOMFLY-PT polynomial	$z^{6}a^{-6}+4z^{6}a^{-8}+4z^{6}a^{-10}+2z^{4}a^{-6}+12z^{4}a^{-8}+10z^{4}a^{-10}-8z^{4}a^{-12}+z^{2}a^{-6}+12z^{2}a^{-8}+8z^{2}a^{-10}-18z^{2}a^{-12}+5z^{2}a^{-14}+4a^{-8}+2a^{-10}-10a^{-12}+6a^{-14}-a^{-16}$
Kauffman polynomial	$z^{12}a^{-12}+z^{12}a^{-14}+6z^{11}a^{-11}+11z^{11}a^{-13}+5z^{11}a^{-15}+13z^{10}a^{-10}+32z^{10}a^{-12}+29z^{10}a^{-14}+10z^{10}a^{-16}+14z^{9}a^{-9}+26z^{9}a^{-11}+26z^{9}a^{-13}+24z^{9}a^{-15}+10z^{9}a^{-17}+10z^{8}a^{-8}-10z^{8}a^{-10}-66z^{8}a^{-12}-60z^{8}a^{-14}-9z^{8}a^{-16}+5z^{8}a^{-18}+4z^{7}a^{-7}-22z^{7}a^{-9}-88z^{7}a^{-11}-134z^{7}a^{-13}-98z^{7}a^{-15}-25z^{7}a^{-17}+z^{7}a^{-19}+z^{6}a^{-6}-20z^{6}a^{-8}-9z^{6}a^{-10}+43z^{6}a^{-12}+17z^{6}a^{-14}-27z^{6}a^{-16}-13z^{6}a^{-18}-6z^{5}a^{-7}+12z^{5}a^{-9}+103z^{5}a^{-11}+179z^{5}a^{-13}+117z^{5}a^{-15}+21z^{5}a^{-17}-2z^{5}a^{-19}-2z^{4}a^{-6}+21z^{4}a^{-8}+10z^{4}a^{-10}-21z^{4}a^{-12}+20z^{4}a^{-14}+39z^{4}a^{-16}+11z^{4}a^{-18}+2z^{3}a^{-7}-62z^{3}a^{-11}-118z^{3}a^{-13}-68z^{3}a^{-15}-9z^{3}a^{-17}+z^{3}a^{-19}+z^{2}a^{-6}-14z^{2}a^{-8}+21z^{2}a^{-12}-4z^{2}a^{-14}-13z^{2}a^{-16}-3z^{2}a^{-18}-2za^{-9}+17za^{-11}+35za^{-13}+19za^{-15}+3za^{-17}+4a^{-8}-2a^{-10}-10a^{-12}-6a^{-14}-a^{-16}$