K12a1230
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-10 q^6+18 q^5-26 q^4+32 q^3-34 q^2+32 q-25+18 q^{-1} -10 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-5 t^4+14 t^3-27 t^2+39 t-43+39 t^{-1} -27 t^{-2} +14 t^{-3} -5 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+5 z^8+9 z^6+7 z^4+2 z^2+1 }[/math] |
| Determinant | 215 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-2} +7 z^8 a^{-2} -z^8 a^{-4} -z^8+19 z^6 a^{-2} -5 z^6 a^{-4} -5 z^6+25 z^4 a^{-2} -9 z^4 a^{-4} -9 z^4+16 z^2 a^{-2} -7 z^2 a^{-4} -7 z^2+4 a^{-2} -2 a^{-4} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +16 z^{10} a^{-2} +9 z^{10} a^{-4} +7 z^{10}+7 a z^9+8 z^9 a^{-1} +14 z^9 a^{-3} +13 z^9 a^{-5} +4 a^2 z^8-36 z^8 a^{-2} -6 z^8 a^{-4} +13 z^8 a^{-6} -13 z^8+a^3 z^7-18 a z^7-33 z^7 a^{-1} -40 z^7 a^{-3} -17 z^7 a^{-5} +9 z^7 a^{-7} -12 a^2 z^6+33 z^6 a^{-2} -3 z^6 a^{-4} -19 z^6 a^{-6} +4 z^6 a^{-8} +z^6-3 a^3 z^5+10 a z^5+25 z^5 a^{-1} +33 z^5 a^{-3} +8 z^5 a^{-5} -12 z^5 a^{-7} +z^5 a^{-9} +11 a^2 z^4-32 z^4 a^{-2} -5 z^4 a^{-4} +12 z^4 a^{-6} -4 z^4 a^{-8} +3 a^3 z^3+2 a z^3-8 z^3 a^{-1} -17 z^3 a^{-3} -2 z^3 a^{-5} +7 z^3 a^{-7} -z^3 a^{-9} -3 a^2 z^2+19 z^2 a^{-2} +7 z^2 a^{-4} -2 z^2 a^{-6} +z^2 a^{-8} +6 z^2-a^3 z-a z+2 z a^{-1} +4 z a^{-3} +z a^{-5} -z a^{-7} -4 a^{-2} -2 a^{-4} -1 }[/math] |
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