K12a353
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+5 q^9-11 q^8+17 q^7-24 q^6+28 q^5-29 q^4+27 q^3-20 q^2+14 q-7+3 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-19 t^2+43 t-55+43 t^{-1} -19 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+5 z^4+3 z^2+1 }[/math] |
| Determinant | 187 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} +z^6 a^{-6} +2 z^4 a^{-2} +5 z^4 a^{-4} -z^4 a^{-8} -z^4+3 z^2 a^{-2} +6 z^2 a^{-4} -4 z^2 a^{-6} -2 z^2+2 a^{-2} +3 a^{-4} -4 a^{-6} + a^{-8} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-5} +2 z^{11} a^{-7} +5 z^{10} a^{-4} +12 z^{10} a^{-6} +7 z^{10} a^{-8} +7 z^9 a^{-3} +11 z^9 a^{-5} +13 z^9 a^{-7} +9 z^9 a^{-9} +7 z^8 a^{-2} +3 z^8 a^{-4} -21 z^8 a^{-6} -12 z^8 a^{-8} +5 z^8 a^{-10} +5 z^7 a^{-1} -5 z^7 a^{-3} -29 z^7 a^{-5} -47 z^7 a^{-7} -27 z^7 a^{-9} +z^7 a^{-11} -8 z^6 a^{-2} -22 z^6 a^{-4} -5 z^6 a^{-6} -8 z^6 a^{-8} -14 z^6 a^{-10} +3 z^6+a z^5-5 z^5 a^{-1} -4 z^5 a^{-3} +12 z^5 a^{-5} +32 z^5 a^{-7} +20 z^5 a^{-9} -2 z^5 a^{-11} +4 z^4 a^{-2} +26 z^4 a^{-4} +20 z^4 a^{-6} +12 z^4 a^{-8} +9 z^4 a^{-10} -5 z^4-2 a z^3+8 z^3 a^{-3} +12 z^3 a^{-5} +4 z^3 a^{-7} -z^3 a^{-9} +z^3 a^{-11} +z^2 a^{-2} -12 z^2 a^{-4} -12 z^2 a^{-6} -2 z^2 a^{-8} +3 z^2+a z+z a^{-1} -2 z a^{-3} -8 z a^{-5} -8 z a^{-7} -2 z a^{-9} -2 a^{-2} +3 a^{-4} +4 a^{-6} + a^{-8} -1 }[/math] |
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