K12n67
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{-1} -2 q^{-2} +5 q^{-3} -7 q^{-4} +8 q^{-5} -8 q^{-6} +8 q^{-7} -6 q^{-8} +4 q^{-9} -2 q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+5 t^3-8 t^2+8 t-7+8 t^{-1} -8 t^{-2} +5 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^6+2 z^4+5 z^2+1 }[/math] |
| Determinant | 51 |
| Signature | -6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^{12}-z^4 a^{10}-6 z^2 a^{10}-6 a^{10}+2 z^6 a^8+11 z^4 a^8+18 z^2 a^8+10 a^8-z^8 a^6-6 z^6 a^6-13 z^4 a^6-15 z^2 a^6-8 a^6+z^6 a^4+5 z^4 a^4+8 z^2 a^4+4 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^4 a^{12}-2 z^2 a^{12}+a^{12}+3 z^7 a^{11}-13 z^5 a^{11}+16 z^3 a^{11}-6 z a^{11}+6 z^8 a^{10}-29 z^6 a^{10}+43 z^4 a^{10}-27 z^2 a^{10}+6 a^{10}+4 z^9 a^9-13 z^7 a^9-z^5 a^9+18 z^3 a^9-7 z a^9+z^{10} a^8+6 z^8 a^8-47 z^6 a^8+77 z^4 a^8-47 z^2 a^8+10 a^8+6 z^9 a^7-26 z^7 a^7+27 z^5 a^7-5 z^3 a^7-z a^7+z^{10} a^6+z^8 a^6-24 z^6 a^6+48 z^4 a^6-34 z^2 a^6+8 a^6+2 z^9 a^5-10 z^7 a^5+15 z^5 a^5-7 z^3 a^5+z^8 a^4-6 z^6 a^4+13 z^4 a^4-12 z^2 a^4+4 a^4 }[/math] |
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