K12n58
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 3 q^{-2} -7 q^{-3} +13 q^{-4} -18 q^{-5} +21 q^{-6} -21 q^{-7} +19 q^{-8} -14 q^{-9} +8 q^{-10} -4 q^{-11} + q^{-12} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+13 t^2-30 t+39-30 t^{-1} +13 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+z^4+4 z^2+1 }[/math] |
| Determinant | 129 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^{12}-4 z^2 a^{10}-5 a^{10}+5 z^4 a^8+12 z^2 a^8+8 a^8-2 z^6 a^6-7 z^4 a^6-11 z^2 a^6-7 a^6+3 z^4 a^4+7 z^2 a^4+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}+6 z^4 a^{12}-2 z^2 a^{12}+a^{12}+4 z^9 a^{11}+5 z^7 a^{11}-32 z^5 a^{11}+30 z^3 a^{11}-9 z a^{11}+z^{10} a^{10}+17 z^8 a^{10}-47 z^6 a^{10}+43 z^4 a^{10}-22 z^2 a^{10}+5 a^{10}+9 z^9 a^9-3 z^7 a^9-29 z^5 a^9+32 z^3 a^9-9 z a^9+z^{10} a^8+18 z^8 a^8-50 z^6 a^8+59 z^4 a^8-35 z^2 a^8+8 a^8+5 z^9 a^7-z^7 a^7-7 z^5 a^7+9 z^3 a^7-3 z a^7+7 z^8 a^6-16 z^6 a^6+30 z^4 a^6-26 z^2 a^6+7 a^6+3 z^7 a^5-z^3 a^5-z a^5+6 z^4 a^4-10 z^2 a^4+4 a^4 }[/math] |
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