K12n243
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{12}+q^8-q^7+2 q^6-q^5+q^4 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-3 t^3+t^2+2 t-3+2 t^{-1} + t^{-2} -3 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+13 z^6+23 z^4+11 z^2+1 }[/math] |
| Determinant | 5 |
| Signature | 8 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +z^8 a^{-10} +7 z^6 a^{-8} +7 z^6 a^{-10} -z^6 a^{-12} +15 z^4 a^{-8} +15 z^4 a^{-10} -7 z^4 a^{-12} +11 z^2 a^{-8} +12 z^2 a^{-10} -13 z^2 a^{-12} +z^2 a^{-14} +2 a^{-8} +4 a^{-10} -7 a^{-12} +2 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-10} +z^{10} a^{-12} +z^9 a^{-9} +2 z^9 a^{-11} +z^9 a^{-13} +z^8 a^{-8} -7 z^8 a^{-10} -8 z^8 a^{-12} -6 z^7 a^{-9} -14 z^7 a^{-11} -8 z^7 a^{-13} -7 z^6 a^{-8} +16 z^6 a^{-10} +23 z^6 a^{-12} +9 z^5 a^{-9} +30 z^5 a^{-11} +21 z^5 a^{-13} +15 z^4 a^{-8} -18 z^4 a^{-10} -34 z^4 a^{-12} -z^4 a^{-14} -2 z^3 a^{-9} -25 z^3 a^{-11} -23 z^3 a^{-13} -11 z^2 a^{-8} +13 z^2 a^{-10} +26 z^2 a^{-12} +2 z^2 a^{-14} -z a^{-9} +8 z a^{-11} +8 z a^{-13} -z a^{-15} +2 a^{-8} -4 a^{-10} -7 a^{-12} -2 a^{-14} }[/math] |
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