K12n30
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 3 q^4-8 q^3+14 q^2-20 q+23-23 q^{-1} +21 q^{-2} -15 q^{-3} +9 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-6 t^3+16 t^2-29 t+37-29 t^{-1} +16 t^{-2} -6 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+2 z^6-3 z^2+1 }[/math] |
| Determinant | 141 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-z^6 a^{-2} +5 z^6+a^4 z^4-7 a^2 z^4-4 z^4 a^{-2} +10 z^4+2 a^4 z^2-8 a^2 z^2-7 z^2 a^{-2} +z^2 a^{-4} +9 z^2+a^4-2 a^2-4 a^{-2} +2 a^{-4} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^2 z^{10}+2 z^{10}+6 a^3 z^9+13 a z^9+7 z^9 a^{-1} +7 a^4 z^8+15 a^2 z^8+8 z^8 a^{-2} +16 z^8+4 a^5 z^7-4 a^3 z^7-19 a z^7-8 z^7 a^{-1} +3 z^7 a^{-3} +a^6 z^6-15 a^4 z^6-45 a^2 z^6-16 z^6 a^{-2} -45 z^6-9 a^5 z^5-13 a^3 z^5+7 z^5 a^{-1} +3 z^5 a^{-3} -2 a^6 z^4+10 a^4 z^4+39 a^2 z^4+26 z^4 a^{-2} +6 z^4 a^{-4} +47 z^4+6 a^5 z^3+11 a^3 z^3+6 a z^3-6 z^3 a^{-1} -7 z^3 a^{-3} +a^6 z^2-4 a^4 z^2-16 a^2 z^2-20 z^2 a^{-2} -8 z^2 a^{-4} -23 z^2-a^5 z-2 a^3 z-a z+3 z a^{-1} +3 z a^{-3} +a^4+2 a^2+4 a^{-2} +2 a^{-4} +4 }[/math] |
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