K12a1257
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+9 q^7-16 q^6+24 q^5-30 q^4+32 q^3-30 q^2+25 q-17+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-25 t^2+41 t-47+41 t^{-1} -25 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-5 z^4-z^2+1 }[/math] |
| Determinant | 203 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +z^6-6 z^4 a^{-2} -5 z^4 a^{-4} +3 z^4 a^{-6} +3 z^4-5 z^2 a^{-2} -z^2 a^{-4} +2 z^2 a^{-6} +3 z^2-2 a^{-2} + a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +8 z^{10} a^{-2} +16 z^{10} a^{-4} +8 z^{10} a^{-6} +10 z^9 a^{-1} +10 z^9 a^{-3} +10 z^9 a^{-5} +10 z^9 a^{-7} -12 z^8 a^{-2} -42 z^8 a^{-4} -14 z^8 a^{-6} +8 z^8 a^{-8} +8 z^8+4 a z^7-21 z^7 a^{-1} -42 z^7 a^{-3} -46 z^7 a^{-5} -25 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6+z^6 a^{-2} +43 z^6 a^{-4} +3 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} -17 z^6-8 a z^5+15 z^5 a^{-1} +56 z^5 a^{-3} +65 z^5 a^{-5} +23 z^5 a^{-7} -9 z^5 a^{-9} -2 a^2 z^4+9 z^4 a^{-2} -9 z^4 a^{-4} +10 z^4 a^{-6} +14 z^4 a^{-8} -2 z^4 a^{-10} +10 z^4+3 a z^3-9 z^3 a^{-1} -30 z^3 a^{-3} -32 z^3 a^{-5} -11 z^3 a^{-7} +3 z^3 a^{-9} +a^2 z^2-10 z^2 a^{-2} -4 z^2 a^{-4} -4 z^2 a^{-6} -4 z^2 a^{-8} -5 z^2+2 z a^{-1} +5 z a^{-3} +5 z a^{-5} +2 z a^{-7} +2 a^{-2} + a^{-4} +2 }[/math] |
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