K12n415
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-9 q^6+13 q^5-16 q^4+18 q^3-16 q^2+13 q-8+4 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-10 t^2+24 t-31+24 t^{-1} -10 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+2 z^4+2 z^2+1 }[/math] |
| Determinant | 103 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +2 z^4 a^{-2} +2 z^4 a^{-4} -z^4 a^{-6} -z^4+2 z^2 a^{-2} +2 z^2 a^{-4} -z^2 a^{-6} -z^2+ a^{-2} + a^{-4} - a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +z^9 a^{-1} +6 z^9 a^{-3} +5 z^9 a^{-5} +z^8 a^{-2} +10 z^8 a^{-4} +9 z^8 a^{-6} -11 z^7 a^{-3} -3 z^7 a^{-5} +8 z^7 a^{-7} +z^6 a^{-2} -25 z^6 a^{-4} -18 z^6 a^{-6} +4 z^6 a^{-8} +4 z^6+a z^5+4 z^5 a^{-1} +13 z^5 a^{-3} -5 z^5 a^{-5} -14 z^5 a^{-7} +z^5 a^{-9} -3 z^4 a^{-2} +23 z^4 a^{-4} +14 z^4 a^{-6} -5 z^4 a^{-8} -7 z^4-2 a z^3-9 z^3 a^{-1} -9 z^3 a^{-3} +5 z^3 a^{-5} +6 z^3 a^{-7} -z^3 a^{-9} +z^2 a^{-2} -7 z^2 a^{-4} -6 z^2 a^{-6} +2 z^2+a z+3 z a^{-1} +3 z a^{-3} -z a^{-5} -2 z a^{-7} - a^{-2} + a^{-4} + a^{-6} }[/math] |
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