K12a1210

Symmetrical form

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ q^2-4 q+8-13 q^{-1} +20 q^{-2} -23 q^{-3} +25 q^{-4} -24 q^{-5} +20 q^{-6} -14 q^{-7} +8 q^{-8} -4 q^{-9} + q^{-10} }[/math]
Alexander polynomial	[math]\displaystyle{ -t^5+5 t^4-12 t^3+21 t^2-28 t+31-28 t^{-1} +21 t^{-2} -12 t^{-3} +5 t^{-4} - t^{-5} }[/math]
Conway polynomial	[math]\displaystyle{ -z^{10}-5 z^8-7 z^6-z^4+3 z^2+1 }[/math]
Determinant	165
Signature	-4
HOMFLY-PT polynomial	[math]\displaystyle{ -a^4 z^{10}+a^6 z^8-7 a^4 z^8+a^2 z^8+5 a^6 z^6-17 a^4 z^6+5 a^2 z^6+7 a^6 z^4-15 a^4 z^4+7 a^2 z^4+a^6 z^2+2 a^2 z^2-2 a^6+3 a^4 }[/math]
Kauffman polynomial	[math]\displaystyle{ z^4 a^{12}+4 z^5 a^{11}-2 z^3 a^{11}+8 z^6 a^{10}-6 z^4 a^{10}+z^2 a^{10}+12 z^7 a^9-14 z^5 a^9+4 z^3 a^9+14 z^8 a^8-22 z^6 a^8+7 z^4 a^8+2 z^2 a^8+12 z^9 a^7-18 z^7 a^7-6 z^5 a^7+14 z^3 a^7-4 z a^7+8 z^{10} a^6-11 z^8 a^6-8 z^6 a^6+5 z^4 a^6+2 a^6+3 z^{11} a^5+5 z^9 a^5-33 z^7 a^5+23 z^5 a^5+4 z^3 a^5-5 z a^5+14 z^{10} a^4-53 z^8 a^4+66 z^6 a^4-36 z^4 a^4+3 z^2 a^4+3 a^4+3 z^{11} a^3-3 z^9 a^3-21 z^7 a^3+35 z^5 a^3-12 z^3 a^3-z a^3+6 z^{10} a^2-27 z^8 a^2+40 z^6 a^2-23 z^4 a^2+4 z^2 a^2+4 z^9 a-18 z^7 a+24 z^5 a-8 z^3 a+z^8-4 z^6+4 z^4 }[/math]

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