K12a875
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+6 q^9-15 q^8+26 q^7-38 q^6+46 q^5-49 q^4+46 q^3-36 q^2+25 q-13+5 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 5 t^3-29 t^2+72 t-95+72 t^{-1} -29 t^{-2} +5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 5 z^6+z^4+z^2+1 }[/math] |
| Determinant | 307 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +3 z^6 a^{-4} +z^6 a^{-6} -z^4 a^{-2} +6 z^4 a^{-4} -2 z^4 a^{-6} -z^4 a^{-8} -z^4-z^2 a^{-2} +6 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-8} + a^{-2} +2 a^{-4} -3 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 6 z^{11} a^{-5} +6 z^{11} a^{-7} +19 z^{10} a^{-4} +34 z^{10} a^{-6} +15 z^{10} a^{-8} +27 z^9 a^{-3} +36 z^9 a^{-5} +23 z^9 a^{-7} +14 z^9 a^{-9} +23 z^8 a^{-2} -11 z^8 a^{-4} -68 z^8 a^{-6} -28 z^8 a^{-8} +6 z^8 a^{-10} +13 z^7 a^{-1} -44 z^7 a^{-3} -115 z^7 a^{-5} -94 z^7 a^{-7} -35 z^7 a^{-9} +z^7 a^{-11} -33 z^6 a^{-2} -38 z^6 a^{-4} +13 z^6 a^{-6} +z^6 a^{-8} -12 z^6 a^{-10} +5 z^6+a z^5-11 z^5 a^{-1} +26 z^5 a^{-3} +93 z^5 a^{-5} +80 z^5 a^{-7} +24 z^5 a^{-9} -z^5 a^{-11} +19 z^4 a^{-2} +42 z^4 a^{-4} +29 z^4 a^{-6} +13 z^4 a^{-8} +5 z^4 a^{-10} -2 z^4+2 z^3 a^{-1} -7 z^3 a^{-3} -22 z^3 a^{-5} -15 z^3 a^{-7} -2 z^3 a^{-9} -4 z^2 a^{-2} -14 z^2 a^{-4} -15 z^2 a^{-6} -4 z^2 a^{-8} +z^2 a^{-10} +z a^{-3} -z a^{-5} -4 z a^{-7} -2 z a^{-9} - a^{-2} +2 a^{-4} +3 a^{-6} + a^{-8} }[/math] |
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