K12a331
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+4-8 q^{-1} +15 q^{-2} -21 q^{-3} +26 q^{-4} -28 q^{-5} +26 q^{-6} -21 q^{-7} +15 q^{-8} -8 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+22 t^2-37 t+43-37 t^{-1} +22 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+4 z^2+1 }[/math] |
| Determinant | 177 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^{10}-2 a^{10}+3 z^4 a^8+8 z^2 a^8+5 a^8-3 z^6 a^6-11 z^4 a^6-13 z^2 a^6-6 a^6+z^8 a^4+5 z^6 a^4+11 z^4 a^4+12 z^2 a^4+4 a^4-z^6 a^2-3 z^4 a^2-2 z^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}-4 z^4 a^{12}+z^2 a^{12}+6 z^7 a^{11}-8 z^5 a^{11}+4 z^3 a^{11}-z a^{11}+9 z^8 a^{10}-16 z^6 a^{10}+18 z^4 a^{10}-12 z^2 a^{10}+2 a^{10}+9 z^9 a^9-14 z^7 a^9+11 z^5 a^9-4 z^3 a^9+z a^9+5 z^{10} a^8+6 z^8 a^8-39 z^6 a^8+56 z^4 a^8-31 z^2 a^8+5 a^8+z^{11} a^7+19 z^9 a^7-59 z^7 a^7+66 z^5 a^7-33 z^3 a^7+7 z a^7+9 z^{10} a^6-6 z^8 a^6-42 z^6 a^6+70 z^4 a^6-38 z^2 a^6+6 a^6+z^{11} a^5+16 z^9 a^5-58 z^7 a^5+64 z^5 a^5-31 z^3 a^5+6 z a^5+4 z^{10} a^4+z^8 a^4-36 z^6 a^4+51 z^4 a^4-26 z^2 a^4+4 a^4+6 z^9 a^3-18 z^7 a^3+15 z^5 a^3-6 z^3 a^3+2 z a^3+4 z^8 a^2-14 z^6 a^2+15 z^4 a^2-6 z^2 a^2+z^7 a-3 z^5 a+2 z^3 a }[/math] |
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