# 9 3 (KnotPlot image) See the full Rolfsen Knot Table. Visit 9 3's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 9 3 at Knotilus!

### Knot presentations

 Planar diagram presentation X8291 X12,4,13,3 X18,10,1,9 X10,18,11,17 X14,6,15,5 X16,8,17,7 X2,12,3,11 X4,14,5,13 X6,16,7,15 Gauss code 1, -7, 2, -8, 5, -9, 6, -1, 3, -4, 7, -2, 8, -5, 9, -6, 4, -3 Dowker-Thistlethwaite code 8 12 14 16 18 2 4 6 10 Conway Notation 

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 3 3-genus 3 Bridge index 2 Super bridge index $\{4,6\}$ Nakanishi index 1 Maximal Thurston-Bennequin number [-16] Hyperbolic Volume 4.99486 A-Polynomial See Data:9 3/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $3$ Topological 4 genus $3$ Concordance genus $3$ Rasmussen s-Invariant -6

### Polynomial invariants

 Alexander polynomial $2 t^3-3 t^2+3 t-3+3 t^{-1} -3 t^{-2} +2 t^{-3}$ Conway polynomial $2 z^6+9 z^4+9 z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 19, 6 } Jones polynomial $-q^{12}+q^{11}-2 q^{10}+3 q^9-3 q^8+3 q^7-2 q^6+2 q^5-q^4+q^3$ HOMFLY-PT polynomial (db, data sources) $z^6 a^{-6} +z^6 a^{-8} +5 z^4 a^{-6} +5 z^4 a^{-8} -z^4 a^{-10} +6 z^2 a^{-6} +7 z^2 a^{-8} -4 z^2 a^{-10} + a^{-6} +3 a^{-8} -3 a^{-10}$ Kauffman polynomial (db, data sources) $z^8 a^{-8} +z^8 a^{-10} +z^7 a^{-7} +2 z^7 a^{-9} +z^7 a^{-11} +z^6 a^{-6} -5 z^6 a^{-8} -5 z^6 a^{-10} +z^6 a^{-12} -4 z^5 a^{-7} -8 z^5 a^{-9} -3 z^5 a^{-11} +z^5 a^{-13} -5 z^4 a^{-6} +9 z^4 a^{-8} +11 z^4 a^{-10} -2 z^4 a^{-12} +z^4 a^{-14} +3 z^3 a^{-7} +9 z^3 a^{-9} +4 z^3 a^{-11} -z^3 a^{-13} +z^3 a^{-15} +6 z^2 a^{-6} -9 z^2 a^{-8} -11 z^2 a^{-10} +3 z^2 a^{-12} -z^2 a^{-14} -4 z a^{-9} -z a^{-11} +z a^{-13} -2 z a^{-15} - a^{-6} +3 a^{-8} +3 a^{-10}$ The A2 invariant $q^{-10} + q^{-14} + q^{-18} + q^{-20} + q^{-22} +2 q^{-24} - q^{-30} - q^{-32} - q^{-34} - q^{-36}$ The G2 invariant $q^{-50} + q^{-54} - q^{-56} + q^{-58} +3 q^{-64} -2 q^{-66} +3 q^{-68} - q^{-70} + q^{-72} +2 q^{-74} -3 q^{-76} +3 q^{-78} - q^{-80} + q^{-82} + q^{-84} - q^{-86} +2 q^{-88} + q^{-90} +2 q^{-94} - q^{-96} + q^{-98} +2 q^{-100} -2 q^{-102} +3 q^{-104} - q^{-106} +2 q^{-108} - q^{-112} +2 q^{-114} -2 q^{-116} +3 q^{-118} -2 q^{-120} + q^{-124} -2 q^{-126} + q^{-128} - q^{-130} - q^{-132} + q^{-134} - q^{-136} - q^{-138} - q^{-142} - q^{-146} -2 q^{-148} - q^{-152} - q^{-156} - q^{-160} - q^{-162} - q^{-164} - q^{-166} +2 q^{-168} -2 q^{-170} + q^{-172} + q^{-178} - q^{-180} + q^{-182} - q^{-184} + q^{-186} - q^{-190} + q^{-192} + q^{-196}$