K12a755
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+13 q^7-24 q^6+34 q^5-41 q^4+44 q^3-40 q^2+32 q-21+11 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+11 t^3-31 t^2+57 t-69+57 t^{-1} -31 t^{-2} +11 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-5 z^6-5 z^4+1 }[/math] |
| Determinant | 271 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -3 z^6 a^{-4} +z^6 a^{-6} +z^6-8 z^4 a^{-2} -2 z^4 a^{-4} +2 z^4 a^{-6} +3 z^4-8 z^2 a^{-2} +3 z^2 a^{-4} +z^2 a^{-6} +4 z^2-3 a^{-2} +3 a^{-4} - a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +9 z^{10} a^{-2} +20 z^{10} a^{-4} +11 z^{10} a^{-6} +12 z^9 a^{-1} +26 z^9 a^{-3} +30 z^9 a^{-5} +16 z^9 a^{-7} +4 z^8 a^{-2} -15 z^8 a^{-4} +2 z^8 a^{-6} +12 z^8 a^{-8} +9 z^8+4 a z^7-18 z^7 a^{-1} -62 z^7 a^{-3} -71 z^7 a^{-5} -26 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-38 z^6 a^{-2} -35 z^6 a^{-4} -37 z^6 a^{-6} -21 z^6 a^{-8} +z^6 a^{-10} -17 z^6-7 a z^5+9 z^5 a^{-1} +43 z^5 a^{-3} +46 z^5 a^{-5} +12 z^5 a^{-7} -7 z^5 a^{-9} -2 a^2 z^4+44 z^4 a^{-2} +42 z^4 a^{-4} +29 z^4 a^{-6} +13 z^4 a^{-8} -z^4 a^{-10} +15 z^4+4 a z^3-10 z^3 a^{-3} -12 z^3 a^{-5} -3 z^3 a^{-7} +3 z^3 a^{-9} +a^2 z^2-20 z^2 a^{-2} -16 z^2 a^{-4} -8 z^2 a^{-6} -3 z^2 a^{-8} -8 z^2-a z-z a^{-1} +z a^{-3} +z a^{-5} +3 a^{-2} +3 a^{-4} + a^{-6} +2 }[/math] |
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