K12n869
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+9 q^7-16 q^6+20 q^5-22 q^4+23 q^3-18 q^2+13 q-7+2 q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-12 t^2+32 t-43+32 t^{-1} -12 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+2 z^2+1 }[/math] |
| Determinant | 135 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6 a^{-4} -4 z^4 a^{-2} +7 z^4 a^{-4} -3 z^4 a^{-6} -7 z^2 a^{-2} +12 z^2 a^{-4} -6 z^2 a^{-6} +z^2 a^{-8} +2 z^2-3 a^{-2} +7 a^{-4} -5 a^{-6} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{10} a^{-4} +3 z^{10} a^{-6} +8 z^9 a^{-3} +15 z^9 a^{-5} +7 z^9 a^{-7} +6 z^8 a^{-2} +8 z^8 a^{-4} +9 z^8 a^{-6} +7 z^8 a^{-8} +z^7 a^{-1} -21 z^7 a^{-3} -35 z^7 a^{-5} -9 z^7 a^{-7} +4 z^7 a^{-9} -12 z^6 a^{-2} -35 z^6 a^{-4} -38 z^6 a^{-6} -14 z^6 a^{-8} +z^6 a^{-10} +7 z^5 a^{-1} +33 z^5 a^{-3} +26 z^5 a^{-5} -9 z^5 a^{-7} -9 z^5 a^{-9} +20 z^4 a^{-2} +47 z^4 a^{-4} +38 z^4 a^{-6} +6 z^4 a^{-8} -2 z^4 a^{-10} +3 z^4-10 z^3 a^{-1} -18 z^3 a^{-3} -z^3 a^{-5} +13 z^3 a^{-7} +6 z^3 a^{-9} -14 z^2 a^{-2} -24 z^2 a^{-4} -18 z^2 a^{-6} -3 z^2 a^{-8} +z^2 a^{-10} -4 z^2+z a^{-1} +z a^{-3} -5 z a^{-5} -7 z a^{-7} -2 z a^{-9} +3 a^{-2} +7 a^{-4} +5 a^{-6} + a^{-8} +1 }[/math] |
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