K13a1040
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Polynomial invariants
| Jones polynomial | Data:K13a1040/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -t^4+10 t^3-39 t^2+84 t-107+84 t^{-1} -39 t^{-2} +10 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | Data:K13a1040/Conway Polynomial |
| Determinant | 375 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -3 z^6 a^{-2} +3 z^6 a^{-4} +2 z^6-a^2 z^4-6 z^4 a^{-2} +6 z^4 a^{-4} -3 z^4 a^{-6} +5 z^4-2 a^2 z^2-5 z^2 a^{-2} +5 z^2 a^{-4} -3 z^2 a^{-6} +z^2 a^{-8} +6 z^2-a^2-2 a^{-2} +2 a^{-4} - a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-2} +2 z^{12} a^{-4} +7 z^{11} a^{-1} +16 z^{11} a^{-3} +9 z^{11} a^{-5} +26 z^{10} a^{-2} +33 z^{10} a^{-4} +17 z^{10} a^{-6} +10 z^{10}+8 a z^9+7 z^9 a^{-1} +19 z^9 a^{-5} +18 z^9 a^{-7} +4 a^2 z^8-61 z^8 a^{-2} -69 z^8 a^{-4} -15 z^8 a^{-6} +12 z^8 a^{-8} -15 z^8+a^3 z^7-18 a z^7-44 z^7 a^{-1} -60 z^7 a^{-3} -68 z^7 a^{-5} -28 z^7 a^{-7} +5 z^7 a^{-9} -11 a^2 z^6+39 z^6 a^{-2} +39 z^6 a^{-4} -12 z^6 a^{-6} -19 z^6 a^{-8} +z^6 a^{-10} -3 z^6-3 a^3 z^5+12 a z^5+43 z^5 a^{-1} +63 z^5 a^{-3} +56 z^5 a^{-5} +14 z^5 a^{-7} -7 z^5 a^{-9} +11 a^2 z^4-5 z^4 a^{-2} -5 z^4 a^{-4} +16 z^4 a^{-6} +11 z^4 a^{-8} -z^4 a^{-10} +15 z^4+3 a^3 z^3-a z^3-15 z^3 a^{-1} -24 z^3 a^{-3} -17 z^3 a^{-5} -z^3 a^{-7} +3 z^3 a^{-9} -5 a^2 z^2-5 z^2 a^{-2} -4 z^2 a^{-4} -6 z^2 a^{-6} -2 z^2 a^{-8} -10 z^2-a^3 z-a z+2 z a^{-1} +4 z a^{-3} +z a^{-5} -z a^{-7} +a^2+2 a^{-2} +2 a^{-4} + a^{-6} +3 }[/math] |
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