K12a578
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-6 q^{-1} +12 q^{-2} -17 q^{-3} +22 q^{-4} -24 q^{-5} +23 q^{-6} -19 q^{-7} +14 q^{-8} -8 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+19 t^2-30 t+35-30 t^{-1} +19 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+11 z^4+6 z^2+1 }[/math] |
| Determinant | 153 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-4 z^4 a^8-6 z^2 a^8-3 a^8+z^8 a^6+5 z^6 a^6+10 z^4 a^6+10 z^2 a^6+4 a^6+z^8 a^4+5 z^6 a^4+9 z^4 a^4+6 z^2 a^4-z^6 a^2-4 z^4 a^2-4 z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-2 z^3 a^{13}+z a^{13}+3 z^6 a^{12}-4 z^4 a^{12}+z^2 a^{12}+6 z^7 a^{11}-9 z^5 a^{11}+6 z^3 a^{11}-2 z a^{11}+8 z^8 a^{10}-13 z^6 a^{10}+12 z^4 a^{10}-6 z^2 a^{10}+7 z^9 a^9-8 z^7 a^9+3 z^5 a^9+z^3 a^9+4 z^{10} a^8+z^8 a^8-7 z^6 a^8+7 z^2 a^8-3 a^8+z^{11} a^7+10 z^9 a^7-26 z^7 a^7+27 z^5 a^7-18 z^3 a^7+6 z a^7+7 z^{10} a^6-14 z^8 a^6+15 z^6 a^6-22 z^4 a^6+16 z^2 a^6-4 a^6+z^{11} a^5+7 z^9 a^5-26 z^7 a^5+31 z^5 a^5-21 z^3 a^5+5 z a^5+3 z^{10} a^4-4 z^8 a^4-6 z^6 a^4+9 z^4 a^4-4 z^2 a^4+4 z^9 a^3-13 z^7 a^3+13 z^5 a^3-6 z^3 a^3+2 z a^3+3 z^8 a^2-12 z^6 a^2+15 z^4 a^2-6 z^2 a^2+z^7 a-4 z^5 a+4 z^3 a }[/math] |
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