K12a375
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+2-4 q^{-1} +9 q^{-2} -12 q^{-3} +16 q^{-4} -18 q^{-5} +18 q^{-6} -15 q^{-7} +11 q^{-8} -7 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-7 t^3+15 t^2-22 t+25-22 t^{-1} +15 t^{-2} -7 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+9 z^6+13 z^4+7 z^2+1 }[/math] |
| Determinant | 117 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-4 z^4 a^8-5 z^2 a^8-2 a^8+z^8 a^6+5 z^6 a^6+8 z^4 a^6+4 z^2 a^6+z^8 a^4+6 z^6 a^4+14 z^4 a^4+15 z^2 a^4+5 a^4-z^6 a^2-5 z^4 a^2-7 z^2 a^2-2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-2 z^3 a^{13}+z a^{13}+3 z^6 a^{12}-5 z^4 a^{12}+z^2 a^{12}+5 z^7 a^{11}-8 z^5 a^{11}+3 z^3 a^{11}-2 z a^{11}+6 z^8 a^{10}-11 z^6 a^{10}+9 z^4 a^{10}-4 z^2 a^{10}+5 z^9 a^9-8 z^7 a^9+5 z^5 a^9+2 z^3 a^9-z a^9+3 z^{10} a^8-3 z^8 a^8+z^6 a^8-z^4 a^8+7 z^2 a^8-2 a^8+z^{11} a^7+3 z^9 a^7-10 z^7 a^7+11 z^5 a^7-3 z^3 a^7+z a^7+5 z^{10} a^6-16 z^8 a^6+26 z^6 a^6-23 z^4 a^6+7 z^2 a^6+z^{11} a^5-3 z^7 a^5+2 z^3 a^5-3 z a^5+2 z^{10} a^4-5 z^8 a^4+2 z^6 a^4+5 z^4 a^4-13 z^2 a^4+5 a^4+2 z^9 a^3-5 z^7 a^3-2 z^5 a^3+9 z^3 a^3-4 z a^3+2 z^8 a^2-9 z^6 a^2+13 z^4 a^2-8 z^2 a^2+2 a^2+z^7 a-5 z^5 a+7 z^3 a-2 z a }[/math] |
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