K12n597
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+3 q^5-7 q^4+10 q^3-11 q^2+13 q-11+9 q^{-1} -6 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-8 t^2+17 t-21+17 t^{-1} -8 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+4 z^4+3 z^2+1 }[/math] |
| Determinant | 75 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6-a^2 z^4+3 z^4 a^{-2} -z^4 a^{-4} +3 z^4-2 a^2 z^2+4 z^2 a^{-2} -2 z^2 a^{-4} +3 z^2-a^2+3 a^{-2} -2 a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+4 a z^9+8 z^9 a^{-1} +4 z^9 a^{-3} +3 a^2 z^8-2 z^8 a^{-2} +3 z^8 a^{-4} -2 z^8+a^3 z^7-15 a z^7-30 z^7 a^{-1} -13 z^7 a^{-3} +z^7 a^{-5} -12 a^2 z^6-8 z^6 a^{-2} -7 z^6 a^{-4} -13 z^6-4 a^3 z^5+14 a z^5+34 z^5 a^{-1} +17 z^5 a^{-3} +z^5 a^{-5} +13 a^2 z^4+10 z^4 a^{-2} +8 z^4 a^{-4} +3 z^4 a^{-6} +18 z^4+4 a^3 z^3-4 a z^3-17 z^3 a^{-1} -10 z^3 a^{-3} +z^3 a^{-7} -5 a^2 z^2-z^2 a^{-2} -2 z^2 a^{-6} -8 z^2-a^3 z+3 z a^{-1} +4 z a^{-3} +z a^{-5} -z a^{-7} +a^2-3 a^{-2} -2 a^{-4} +1 }[/math] |
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