# 10 8 (KnotPlot image) See the full Rolfsen Knot Table. Visit 10 8's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 8 at Knotilus!

### Knot presentations

 Planar diagram presentation X1627 X7,16,8,17 X5,13,6,12 X3,15,4,14 X13,5,14,4 X15,3,16,2 X9,18,10,19 X11,20,12,1 X17,8,18,9 X19,10,20,11 Gauss code -1, 6, -4, 5, -3, 1, -2, 9, -7, 10, -8, 3, -5, 4, -6, 2, -9, 7, -10, 8 Dowker-Thistlethwaite code 6 14 12 16 18 20 4 2 8 10 Conway Notation 

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 2 3-genus 3 Bridge index 2 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-11][-1] Hyperbolic Volume 6.08323 A-Polynomial See Data:10 8/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $2$ Topological 4 genus $2$ Concordance genus $3$ Rasmussen s-Invariant -4

### Polynomial invariants

 Alexander polynomial $-2 t^3+5 t^2-5 t+5-5 t^{-1} +5 t^{-2} -2 t^{-3}$ Conway polynomial $-2 z^6-7 z^4-3 z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 29, -4 } Jones polynomial $q^2-q+2-3 q^{-1} +4 q^{-2} -4 q^{-3} +4 q^{-4} -4 q^{-5} +3 q^{-6} -2 q^{-7} + q^{-8}$ HOMFLY-PT polynomial (db, data sources) $z^4 a^6+3 z^2 a^6+a^6-z^6 a^4-4 z^4 a^4-3 z^2 a^4-z^6 a^2-5 z^4 a^2-7 z^2 a^2-3 a^2+z^4+4 z^2+3$ Kauffman polynomial (db, data sources) $z^2 a^{10}+2 z^3 a^9+3 z^4 a^8-2 z^2 a^8+4 z^5 a^7-7 z^3 a^7+2 z a^7+4 z^6 a^6-10 z^4 a^6+5 z^2 a^6-a^6+3 z^7 a^5-8 z^5 a^5+2 z^3 a^5+z a^5+2 z^8 a^4-6 z^6 a^4+z^4 a^4+3 z^2 a^4+z^9 a^3-3 z^7 a^3-z^5 a^3+5 z^3 a^3-z a^3+3 z^8 a^2-17 z^6 a^2+30 z^4 a^2-18 z^2 a^2+3 a^2+z^9 a-6 z^7 a+11 z^5 a-6 z^3 a+z^8-7 z^6+16 z^4-13 z^2+3$ The A2 invariant $q^{24}+q^{14}-q^{12}-q^8-q^6+1+ q^{-2} + q^{-4} + q^{-6}$ The G2 invariant $q^{134}-q^{132}+q^{130}-q^{128}-q^{122}+2 q^{120}-2 q^{118}+2 q^{116}-2 q^{114}+q^{110}-q^{108}+3 q^{106}-3 q^{104}+2 q^{102}-q^{100}-q^{98}+2 q^{96}-3 q^{94}+3 q^{92}-2 q^{90}+q^{88}+q^{86}-q^{84}+2 q^{82}+q^{78}+q^{74}+2 q^{70}+q^{68}+q^{66}+q^{62}-q^{60}-3 q^{54}+3 q^{52}-5 q^{50}+3 q^{48}-q^{46}-5 q^{44}+5 q^{42}-7 q^{40}+2 q^{38}-2 q^{36}-2 q^{34}+2 q^{32}-3 q^{30}+3 q^{28}-q^{26}-2 q^{20}+q^{18}+q^{16}-q^{14}+2 q^{12}-3 q^{10}+3 q^8+q^6-3 q^4+6 q^2-6+4 q^{-2} + q^{-4} -3 q^{-6} +6 q^{-8} -4 q^{-10} +4 q^{-12} +2 q^{-18} -2 q^{-20} +2 q^{-22} + q^{-26}$