K12n230
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-2 q^7+2 q^6-q^5-q^4+3 q^3-4 q^2+5 q-5+4 q^{-1} -2 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-4 t^2+4 t-1+4 t^{-1} -4 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6+2 z^4-3 z^2+1 }[/math] |
| Determinant | 19 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +4 z^4 a^{-2} -2 z^4+a^2 z^2+4 z^2 a^{-2} -2 z^2 a^{-6} -6 z^2+2 a^2+2 a^{-2} + a^{-4} -2 a^{-6} + a^{-8} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +z^9 a^{-3} +3 z^9 a^{-5} +2 z^9 a^{-7} -7 z^8 a^{-4} -5 z^8 a^{-6} +z^8 a^{-8} +z^8+2 a z^7+4 z^7 a^{-1} -8 z^7 a^{-3} -23 z^7 a^{-5} -13 z^7 a^{-7} +a^2 z^6+5 z^6 a^{-2} +11 z^6 a^{-4} -6 z^6 a^{-8} +z^6-7 a z^5-11 z^5 a^{-1} +21 z^5 a^{-3} +49 z^5 a^{-5} +24 z^5 a^{-7} -4 a^2 z^4-15 z^4 a^{-2} +16 z^4 a^{-6} +10 z^4 a^{-8} -13 z^4+6 a z^3+3 z^3 a^{-1} -21 z^3 a^{-3} -34 z^3 a^{-5} -16 z^3 a^{-7} +5 a^2 z^2+9 z^2 a^{-2} -4 z^2 a^{-4} -11 z^2 a^{-6} -6 z^2 a^{-8} +13 z^2-a z+z a^{-1} +6 z a^{-3} +8 z a^{-5} +4 z a^{-7} -2 a^2-2 a^{-2} + a^{-4} +2 a^{-6} + a^{-8} -3 }[/math] |
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