7 6

[[Image:7_5.{{{ext}}}|80px|link=7_5]] 7_5

[[Image:7_7.{{{ext}}}|80px|link=7_7]] 7_7

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Knot presentations

Planar diagram presentation	X1425 X3849 X5,12,6,13 X9,1,10,14 X13,11,14,10 X11,6,12,7 X7283
Gauss code	-1, 7, -2, 1, -3, 6, -7, 2, -4, 5, -6, 3, -5, 4
Dowker-Thistlethwaite code	4 8 12 2 14 6 10
Conway Notation	[2212]

Three dimensional invariants

Symmetry type Reversible Unknotting number 1 3-genus 2 Bridge index 2 Super bridge index 4 Nakanishi index 1 Maximal Thurston-Bennequin number [-8][-1] Hyperbolic Volume 7.08493 A-Polynomial See Data:7 6/A-polynomial

[edit Notes for 7 6's three dimensional invariants]

Polynomial invariants

Jones polynomial	[math]\displaystyle{ q-2+3 q^{-1} -3 q^{-2} +4 q^{-3} -3 q^{-4} +2 q^{-5} - q^{-6} }[/math]
Alexander polynomial	[math]\displaystyle{ -t^2- t^{-2} +5 t+5 t^{-1} -7 }[/math]
Conway polynomial	[math]\displaystyle{ -z^4+z^2+1 }[/math]
Determinant	19
Signature	-2
HOMFLY-PT polynomial	[math]\displaystyle{ -a^6+2 a^4 z^2+2 a^4-a^2 z^4-2 a^2 z^2-a^2+z^2+1 }[/math]
Kauffman polynomial	[math]\displaystyle{ a^7 z^3-a^7 z+2 a^6 z^4-2 a^6 z^2+a^6+2 a^5 z^5-a^5 z^3+a^4 z^6+2 a^4 z^4-4 a^4 z^2+2 a^4+4 a^3 z^5-6 a^3 z^3+2 a^3 z+a^2 z^6+a^2 z^4-4 a^2 z^2+a^2+2 a z^5-4 a z^3+a z+z^4-2 z^2+1 }[/math]
(other formats)

Vassiliev invariants

V2 and V3:

(1, -2)

V2,1 through V6,9:

V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9 [math]\displaystyle{ 4 }[/math] [math]\displaystyle{ -16 }[/math] [math]\displaystyle{ 8 }[/math] [math]\displaystyle{ \frac{158}{3} }[/math] [math]\displaystyle{ \frac{34}{3} }[/math] [math]\displaystyle{ -64 }[/math] [math]\displaystyle{ -\frac{544}{3} }[/math] [math]\displaystyle{ -\frac{64}{3} }[/math] [math]\displaystyle{ -48 }[/math] [math]\displaystyle{ \frac{32}{3} }[/math] [math]\displaystyle{ 128 }[/math] [math]\displaystyle{ \frac{632}{3} }[/math] [math]\displaystyle{ \frac{136}{3} }[/math] [math]\displaystyle{ \frac{19471}{30} }[/math] [math]\displaystyle{ -\frac{474}{5} }[/math] [math]\displaystyle{ \frac{17342}{45} }[/math] [math]\displaystyle{ \frac{401}{18} }[/math] [math]\displaystyle{ \frac{1711}{30} }[/math]

V_2,1 through V_6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V₂ and V₃.