K12n507
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q-3+7 q^{-1} -9 q^{-2} +12 q^{-3} -13 q^{-4} +11 q^{-5} -9 q^{-6} +6 q^{-7} -3 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-7 t^2+18 t-23+18 t^{-1} -7 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6-z^4-z^2+1 }[/math] |
| Determinant | 75 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-2 z^4 a^6-4 z^2 a^6-2 a^6+z^6 a^4+3 z^4 a^4+4 z^2 a^4+a^4-2 z^4 a^2-3 z^2 a^2+z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^6 a^{10}-3 z^4 a^{10}+z^2 a^{10}+3 z^7 a^9-9 z^5 a^9+4 z^3 a^9-z a^9+5 z^8 a^8-17 z^6 a^8+15 z^4 a^8-7 z^2 a^8+a^8+5 z^9 a^7-18 z^7 a^7+20 z^5 a^7-10 z^3 a^7+2 z a^7+2 z^{10} a^6-z^8 a^6-17 z^6 a^6+32 z^4 a^6-16 z^2 a^6+2 a^6+8 z^9 a^5-34 z^7 a^5+53 z^5 a^5-29 z^3 a^5+7 z a^5+2 z^{10} a^4-5 z^8 a^4+17 z^4 a^4-12 z^2 a^4+a^4+3 z^9 a^3-13 z^7 a^3+27 z^5 a^3-20 z^3 a^3+5 z a^3+z^8 a^2-z^6 a^2+4 z^4 a^2-6 z^2 a^2+3 z^5 a-5 z^3 a+z a+z^4-2 z^2+1 }[/math] |
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