K12a815
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+2 q^3-5 q^2+8 q-10+14 q^{-1} -14 q^{-2} +14 q^{-3} -11 q^{-4} +8 q^{-5} -5 q^{-6} +2 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-3 t^4+7 t^3-12 t^2+16 t-17+16 t^{-1} -12 t^{-2} +7 t^{-3} -3 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+7 z^8+18 z^6+20 z^4+8 z^2+1 }[/math] |
| Determinant | 95 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^{10}-a^4 z^8+9 a^2 z^8-z^8-7 a^4 z^6+32 a^2 z^6-7 z^6-18 a^4 z^4+56 a^2 z^4-18 z^4-20 a^4 z^2+48 a^2 z^2-20 z^2-8 a^4+16 a^2-7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+6 a^2 z^{10}+3 z^{10}+3 a^5 z^9+2 a^3 z^9+2 a z^9+3 z^9 a^{-1} +3 a^6 z^8-12 a^4 z^8-30 a^2 z^8+2 z^8 a^{-2} -13 z^8+3 a^7 z^7-7 a^5 z^7-21 a^3 z^7-24 a z^7-12 z^7 a^{-1} +z^7 a^{-3} +2 a^8 z^6-5 a^6 z^6+29 a^4 z^6+67 a^2 z^6-8 z^6 a^{-2} +23 z^6+a^9 z^5-6 a^7 z^5+10 a^5 z^5+51 a^3 z^5+52 a z^5+13 z^5 a^{-1} -5 z^5 a^{-3} -4 a^8 z^4+4 a^6 z^4-36 a^4 z^4-82 a^2 z^4+7 z^4 a^{-2} -31 z^4-3 a^9 z^3+4 a^7 z^3-5 a^5 z^3-47 a^3 z^3-49 a z^3-7 z^3 a^{-1} +7 z^3 a^{-3} +a^8 z^2-2 a^6 z^2+27 a^4 z^2+55 a^2 z^2-z^2 a^{-2} +24 z^2+2 a^9 z-2 a^7 z+a^5 z+16 a^3 z+16 a z+2 z a^{-1} -3 z a^{-3} -8 a^4-16 a^2-7 }[/math] |
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