K12a240
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-7 q^{-1} +14 q^{-2} -19 q^{-3} +25 q^{-4} -27 q^{-5} +26 q^{-6} -22 q^{-7} +15 q^{-8} -9 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+22 t^2-34 t+39-34 t^{-1} +22 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+7 z^6+8 z^4+5 z^2+1 }[/math] |
| Determinant | 173 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-3 z^4 a^8-2 z^2 a^8+z^8 a^6+4 z^6 a^6+4 z^4 a^6-2 z^2 a^6-4 a^6+z^8 a^4+5 z^6 a^4+11 z^4 a^4+14 z^2 a^4+7 a^4-z^6 a^2-4 z^4 a^2-5 z^2 a^2-2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-5 z^4 a^{12}+z^2 a^{12}+8 z^7 a^{11}-12 z^5 a^{11}+7 z^3 a^{11}-2 z a^{11}+10 z^8 a^{10}-14 z^6 a^{10}+8 z^4 a^{10}-2 z^2 a^{10}+8 z^9 a^9-3 z^7 a^9-13 z^5 a^9+14 z^3 a^9-3 z a^9+4 z^{10} a^8+10 z^8 a^8-31 z^6 a^8+22 z^4 a^8-3 z^2 a^8+z^{11} a^7+13 z^9 a^7-23 z^7 a^7-z^5 a^7+16 z^3 a^7-7 z a^7+7 z^{10} a^6-2 z^8 a^6-25 z^6 a^6+27 z^4 a^6-13 z^2 a^6+4 a^6+z^{11} a^5+9 z^9 a^5-22 z^7 a^5+2 z^5 a^5+17 z^3 a^5-10 z a^5+3 z^{10} a^4+z^8 a^4-23 z^6 a^4+32 z^4 a^4-21 z^2 a^4+7 a^4+4 z^9 a^3-9 z^7 a^3-z^5 a^3+12 z^3 a^3-6 z a^3+3 z^8 a^2-11 z^6 a^2+14 z^4 a^2-8 z^2 a^2+2 a^2+z^7 a-4 z^5 a+5 z^3 a-2 z a }[/math] |
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