K12n345
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+5 q^7-8 q^6+10 q^5-11 q^4+11 q^3-8 q^2+6 q-3+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+4 t^3-8 t^2+13 t-15+13 t^{-1} -8 t^{-2} +4 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-4 z^6-4 z^4+z^2+1 }[/math] |
| Determinant | 67 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-4} +z^6 a^{-2} -6 z^6 a^{-4} +z^6 a^{-6} +4 z^4 a^{-2} -12 z^4 a^{-4} +4 z^4 a^{-6} +5 z^2 a^{-2} -8 z^2 a^{-4} +4 z^2 a^{-6} +2 a^{-2} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +z^9 a^{-3} +4 z^9 a^{-5} +3 z^9 a^{-7} -3 z^8 a^{-4} +z^8 a^{-6} +4 z^8 a^{-8} -2 z^7 a^{-3} -13 z^7 a^{-5} -8 z^7 a^{-7} +3 z^7 a^{-9} +5 z^6 a^{-2} +11 z^6 a^{-4} -8 z^6 a^{-6} -13 z^6 a^{-8} +z^6 a^{-10} +3 z^5 a^{-1} +9 z^5 a^{-3} +20 z^5 a^{-5} +4 z^5 a^{-7} -10 z^5 a^{-9} -8 z^4 a^{-2} -14 z^4 a^{-4} +8 z^4 a^{-6} +10 z^4 a^{-8} -3 z^4 a^{-10} +z^4-4 z^3 a^{-1} -10 z^3 a^{-3} -11 z^3 a^{-5} +2 z^3 a^{-7} +7 z^3 a^{-9} +5 z^2 a^{-2} +8 z^2 a^{-4} -z^2 a^{-6} -2 z^2 a^{-8} +z^2 a^{-10} -z^2+z a^{-1} +3 z a^{-3} +z a^{-5} -2 z a^{-7} -z a^{-9} -2 a^{-2} - a^{-4} }[/math] |
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