K12a405
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+10 q^7-17 q^6+24 q^5-29 q^4+30 q^3-28 q^2+22 q-14+8 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-19 t^2+45 t-57+45 t^{-1} -19 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6-z^4-4 z^2+1 }[/math] |
| Determinant | 191 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} -z^4 a^{-2} +5 z^4 a^{-4} -3 z^4 a^{-6} -2 z^4+a^2 z^2-5 z^2 a^{-2} +6 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-8} -2 z^2+a^2-3 a^{-2} +3 a^{-4} -2 a^{-6} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +5 z^{10} a^{-2} +12 z^{10} a^{-4} +7 z^{10} a^{-6} +6 z^9 a^{-1} +10 z^9 a^{-3} +14 z^9 a^{-5} +10 z^9 a^{-7} -3 z^8 a^{-2} -23 z^8 a^{-4} -7 z^8 a^{-6} +8 z^8 a^{-8} +5 z^8+3 a z^7-9 z^7 a^{-1} -33 z^7 a^{-3} -47 z^7 a^{-5} -22 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-8 z^6 a^{-2} +11 z^6 a^{-4} -9 z^6 a^{-6} -17 z^6 a^{-8} +z^6 a^{-10} -9 z^6-7 a z^5+4 z^5 a^{-1} +40 z^5 a^{-3} +55 z^5 a^{-5} +18 z^5 a^{-7} -8 z^5 a^{-9} -3 a^2 z^4+15 z^4 a^{-2} +13 z^4 a^{-4} +16 z^4 a^{-6} +10 z^4 a^{-8} -2 z^4 a^{-10} +3 z^4+4 a z^3-4 z^3 a^{-1} -17 z^3 a^{-3} -24 z^3 a^{-5} -12 z^3 a^{-7} +3 z^3 a^{-9} +3 a^2 z^2-12 z^2 a^{-2} -11 z^2 a^{-4} -9 z^2 a^{-6} -5 z^2 a^{-8} +z^2 a^{-10} -z^2+z a^{-1} +z a^{-3} +3 z a^{-5} +3 z a^{-7} -a^2+3 a^{-2} +3 a^{-4} +2 a^{-6} + a^{-8} +1 }[/math] |
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