K13a1027
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Polynomial invariants
| Jones polynomial | Data:K13a1027/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+14 t^3-42 t^2+77 t-93+77 t^{-1} -42 t^{-2} +14 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a1027/Conway Polynomial |
| Determinant | 363 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -2 z^6 a^{-2} -3 z^6 a^{-4} +z^6 a^{-6} +2 z^6-a^2 z^4-4 z^4 a^{-4} +2 z^4 a^{-6} +5 z^4-2 a^2 z^2+3 z^2 a^{-2} -3 z^2 a^{-4} +z^2 a^{-6} +4 z^2-a^2+3 a^{-2} -2 a^{-4} +1 }[/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+6 z^9 a^{-1} -3 z^9 a^{-3} +17 z^9 a^{-5} +18 z^9 a^{-7} +4 a^2 z^8-71 z^8 a^{-2} -82 z^8 a^{-4} -20 z^8 a^{-6} +12 z^8 a^{-8} -17 z^8+a^3 z^7-19 a z^7-50 z^7 a^{-1} -70 z^7 a^{-3} -77 z^7 a^{-5} -32 z^7 a^{-7} +5 z^7 a^{-9} -11 a^2 z^6+61 z^6 a^{-2} +66 z^6 a^{-4} -4 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} +z^6-3 a^3 z^5+14 a z^5+63 z^5 a^{-1} +103 z^5 a^{-3} +85 z^5 a^{-5} +21 z^5 a^{-7} -7 z^5 a^{-9} +10 a^2 z^4-20 z^4 a^{-2} -19 z^4 a^{-4} +11 z^4 a^{-6} +10 z^4 a^{-8} -z^4 a^{-10} +9 z^4+3 a^3 z^3-5 a z^3-36 z^3 a^{-1} -57 z^3 a^{-3} -39 z^3 a^{-5} -8 z^3 a^{-7} +2 z^3 a^{-9} -4 a^2 z^2+3 z^2 a^{-2} +4 z^2 a^{-4} -3 z^2 a^{-6} -2 z^2 a^{-8} -6 z^2-a^3 z+a z+8 z a^{-1} +13 z a^{-3} +8 z a^{-5} +z a^{-7} +a^2-3 a^{-2} -2 a^{-4} +1 }[/math] |
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