K12n510
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^{-2} -6 q^{-3} +12 q^{-4} -16 q^{-5} +20 q^{-6} -20 q^{-7} +18 q^{-8} -14 q^{-9} +8 q^{-10} -4 q^{-11} + q^{-12} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^3+11 t^2-29 t+39-29 t^{-1} +11 t^{-2} - t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^6+5 z^4+6 z^2+1 }[/math] |
| Determinant | 121 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^{12}-4 z^2 a^{10}-4 a^{10}+4 z^4 a^8+7 z^2 a^8+3 a^8-z^6 a^6-z^4 a^6+2 z^4 a^4+3 z^2 a^4+a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^6 a^{14}-2 z^4 a^{14}+z^2 a^{14}+4 z^7 a^{13}-10 z^5 a^{13}+8 z^3 a^{13}-2 z a^{13}+6 z^8 a^{12}-12 z^6 a^{12}+5 z^4 a^{12}+a^{12}+4 z^9 a^{11}+4 z^7 a^{11}-30 z^5 a^{11}+30 z^3 a^{11}-10 z a^{11}+z^{10} a^{10}+14 z^8 a^{10}-34 z^6 a^{10}+23 z^4 a^{10}-11 z^2 a^{10}+4 a^{10}+7 z^9 a^9+3 z^7 a^9-32 z^5 a^9+28 z^3 a^9-8 z a^9+z^{10} a^8+11 z^8 a^8-19 z^6 a^8+11 z^4 a^8-7 z^2 a^8+3 a^8+3 z^9 a^7+4 z^7 a^7-7 z^5 a^7+2 z^3 a^7+3 z^8 a^6+2 z^6 a^6-2 z^4 a^6+z^7 a^5+5 z^5 a^5-4 z^3 a^5+3 z^4 a^4-3 z^2 a^4+a^4 }[/math] |
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