K12a472
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 1-5 q^{-1} +13 q^{-2} -21 q^{-3} +30 q^{-4} -36 q^{-5} +38 q^{-6} -34 q^{-7} +27 q^{-8} -18 q^{-9} +9 q^{-10} -4 q^{-11} + q^{-12} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+22 t^2-56 t+75-56 t^{-1} +22 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6+4 z^4+5 z^2+1 }[/math] |
| Determinant | 237 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^{12}-4 z^2 a^{10}-4 a^{10}+5 z^4 a^8+8 z^2 a^8+4 a^8-2 z^6 a^6-3 z^4 a^6-3 z^2 a^6-2 a^6-z^6 a^4+z^4 a^4+4 z^2 a^4+2 a^4+z^4 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^6 a^{14}-2 z^4 a^{14}+z^2 a^{14}+4 z^7 a^{13}-9 z^5 a^{13}+7 z^3 a^{13}-2 z a^{13}+7 z^8 a^{12}-12 z^6 a^{12}+5 z^4 a^{12}-z^2 a^{12}+a^{12}+8 z^9 a^{11}-6 z^7 a^{11}-14 z^5 a^{11}+19 z^3 a^{11}-8 z a^{11}+7 z^{10} a^{10}-z^8 a^{10}-17 z^6 a^{10}+21 z^4 a^{10}-15 z^2 a^{10}+4 a^{10}+3 z^{11} a^9+14 z^9 a^9-37 z^7 a^9+25 z^5 a^9+3 z^3 a^9-5 z a^9+18 z^{10} a^8-31 z^8 a^8+7 z^6 a^8+22 z^4 a^8-17 z^2 a^8+4 a^8+3 z^{11} a^7+22 z^9 a^7-68 z^7 a^7+64 z^5 a^7-18 z^3 a^7+z a^7+11 z^{10} a^6-11 z^8 a^6-14 z^6 a^6+21 z^4 a^6-9 z^2 a^6+2 a^6+16 z^9 a^5-36 z^7 a^5+27 z^5 a^5-9 z^3 a^5+12 z^8 a^4-24 z^6 a^4+12 z^4 a^4-5 z^2 a^4+2 a^4+5 z^7 a^3-7 z^5 a^3+z^6 a^2-z^4 a^2 }[/math] |
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