K12a562
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+8 q^7-14 q^6+21 q^5-25 q^4+27 q^3-25 q^2+20 q-14+8 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-15 t^2+41 t-55+41 t^{-1} -15 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-3 z^4-z^2+1 }[/math] |
| Determinant | 171 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +z^4 a^{-4} -2 z^4 a^{-6} -2 z^4+a^2 z^2-2 z^2 a^{-2} +3 z^2 a^{-4} -2 z^2 a^{-6} +z^2 a^{-8} -2 z^2+a^2-2 a^{-2} +3 a^{-4} - a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +4 z^{10} a^{-2} +8 z^{10} a^{-4} +4 z^{10} a^{-6} +6 z^9 a^{-1} +13 z^9 a^{-3} +14 z^9 a^{-5} +7 z^9 a^{-7} -8 z^8 a^{-4} +4 z^8 a^{-6} +7 z^8 a^{-8} +5 z^8+3 a z^7-11 z^7 a^{-1} -40 z^7 a^{-3} -43 z^7 a^{-5} -13 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-12 z^6 a^{-2} -14 z^6 a^{-4} -31 z^6 a^{-6} -18 z^6 a^{-8} +z^6 a^{-10} -9 z^6-7 a z^5+10 z^5 a^{-1} +55 z^5 a^{-3} +52 z^5 a^{-5} +4 z^5 a^{-7} -10 z^5 a^{-9} -3 a^2 z^4+16 z^4 a^{-2} +35 z^4 a^{-4} +40 z^4 a^{-6} +14 z^4 a^{-8} -2 z^4 a^{-10} +2 z^4+4 a z^3-12 z^3 a^{-1} -38 z^3 a^{-3} -26 z^3 a^{-5} +z^3 a^{-7} +5 z^3 a^{-9} +3 a^2 z^2-12 z^2 a^{-2} -21 z^2 a^{-4} -16 z^2 a^{-6} -5 z^2 a^{-8} +z^2+5 z a^{-1} +10 z a^{-3} +6 z a^{-5} +z a^{-7} -a^2+2 a^{-2} +3 a^{-4} + a^{-6} }[/math] |
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