K12n840
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-4 q^2+9 q-13+18 q^{-1} -20 q^{-2} +19 q^{-3} -16 q^{-4} +11 q^{-5} -6 q^{-6} +2 q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+6 t^3-16 t^2+24 t-25+24 t^{-1} -16 t^{-2} +6 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^6-2 z^2+1 }[/math] |
| Determinant | 119 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^8-z^4 a^6-4 z^2 a^6-3 a^6+2 z^6 a^4+8 z^4 a^4+10 z^2 a^4+5 a^4-z^8 a^2-5 z^6 a^2-10 z^4 a^2-11 z^2 a^2-5 a^2+z^6+3 z^4+3 z^2+3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^4 z^{10}+3 a^2 z^{10}+6 a^5 z^9+14 a^3 z^9+8 a z^9+4 a^6 z^8+a^4 z^8+5 a^2 z^8+8 z^8+a^7 z^7-17 a^5 z^7-44 a^3 z^7-22 a z^7+4 z^7 a^{-1} -6 a^6 z^6-18 a^4 z^6-36 a^2 z^6+z^6 a^{-2} -23 z^6+5 a^7 z^5+31 a^5 z^5+54 a^3 z^5+19 a z^5-9 z^5 a^{-1} +3 a^8 z^4+11 a^6 z^4+36 a^4 z^4+49 a^2 z^4-2 z^4 a^{-2} +19 z^4-9 a^7 z^3-23 a^5 z^3-24 a^3 z^3-8 a z^3+2 z^3 a^{-1} -4 a^8 z^2-12 a^6 z^2-24 a^4 z^2-25 a^2 z^2-9 z^2+3 a^7 z+5 a^5 z+3 a^3 z+a z+a^8+3 a^6+5 a^4+5 a^2+3 }[/math] |
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