K12a313
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+4 q^9-10 q^8+17 q^7-25 q^6+31 q^5-32 q^4+31 q^3-25 q^2+17 q-9+4 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-20 t^2+48 t-63+48 t^{-1} -20 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+4 z^4+4 z^2+1 }[/math] |
| Determinant | 207 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} +z^6 a^{-6} +z^4 a^{-2} +4 z^4 a^{-4} +z^4 a^{-6} -z^4 a^{-8} -z^4+z^2 a^{-2} +4 z^2 a^{-4} +z^2 a^{-6} -z^2 a^{-8} -z^2+2 a^{-4} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-5} +2 z^{11} a^{-7} +7 z^{10} a^{-4} +13 z^{10} a^{-6} +6 z^{10} a^{-8} +11 z^9 a^{-3} +18 z^9 a^{-5} +14 z^9 a^{-7} +7 z^9 a^{-9} +11 z^8 a^{-2} +4 z^8 a^{-4} -18 z^8 a^{-6} -7 z^8 a^{-8} +4 z^8 a^{-10} +8 z^7 a^{-1} -10 z^7 a^{-3} -45 z^7 a^{-5} -47 z^7 a^{-7} -19 z^7 a^{-9} +z^7 a^{-11} -13 z^6 a^{-2} -28 z^6 a^{-4} -12 z^6 a^{-6} -13 z^6 a^{-8} -12 z^6 a^{-10} +4 z^6+a z^5-10 z^5 a^{-1} -5 z^5 a^{-3} +26 z^5 a^{-5} +37 z^5 a^{-7} +14 z^5 a^{-9} -3 z^5 a^{-11} +5 z^4 a^{-2} +26 z^4 a^{-4} +20 z^4 a^{-6} +15 z^4 a^{-8} +11 z^4 a^{-10} -5 z^4-a z^3+5 z^3 a^{-1} +11 z^3 a^{-3} +2 z^3 a^{-5} -9 z^3 a^{-7} -3 z^3 a^{-9} +3 z^3 a^{-11} -10 z^2 a^{-4} -7 z^2 a^{-6} -2 z^2 a^{-8} -3 z^2 a^{-10} +2 z^2-z a^{-1} -3 z a^{-3} -4 z a^{-5} +z a^{-9} -z a^{-11} +2 a^{-4} - a^{-8} }[/math] |
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