7 5

[[Image:7_4.{{{ext}}}|80px|link=7_4]] 7_4

[[Image:7_6.{{{ext}}}|80px|link=7_6]] 7_6

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Knot presentations

Planar diagram presentation	X1425 X3,10,4,11 X5,12,6,13 X7,14,8,1 X13,6,14,7 X11,8,12,9 X9,2,10,3
Gauss code	-1, 7, -2, 1, -3, 5, -4, 6, -7, 2, -6, 3, -5, 4
Dowker-Thistlethwaite code	4 10 12 14 2 8 6
Conway Notation	[322]

Three dimensional invariants

Symmetry type Reversible Unknotting number 2 3-genus 2 Bridge index 2 Super bridge index 4 Nakanishi index 1 Maximal Thurston-Bennequin number Failed to parse (syntax error): {\displaystyle \text{$\$$Failed}} Hyperbolic Volume 6.44354 A-Polynomial See Data:7 5/A-polynomial

[edit Notes for 7 5's three dimensional invariants]

Polynomial invariants

Jones polynomial	$-q^{-9}+2q^{-8}-3q^{-7}+3q^{-6}-3q^{-5}+3q^{-4}-q^{-3}+q^{-2}$
Alexander polynomial	$2t^{2}-4t+5-4t^{-1}+2t^{-2}$
Conway polynomial	$2z^{4}+4z^{2}+1$
Determinant	17
Signature	-4
HOMFLY-PT polynomial	$a^{8}\left(-z^{2}\right)-a^{8}+a^{6}z^{4}+2a^{6}z^{2}+a^{4}z^{4}+3a^{4}z^{2}+2a^{4}$
Kauffman polynomial	$a^{11}z^{3}-a^{11}z+2a^{10}z^{4}-2a^{10}z^{2}+2a^{9}z^{5}-2a^{9}z^{3}+a^{9}z+a^{8}z^{6}+a^{8}z^{2}-a^{8}+3a^{7}z^{5}-4a^{7}z^{3}+a^{7}z+a^{6}z^{6}-a^{6}z^{4}+a^{5}z^{5}-a^{5}z^{3}-a^{5}z+a^{4}z^{4}-3a^{4}z^{2}+2a^{4}$
(other formats)

Vassiliev invariants

V2 and V3:

(4, -8)

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 $16$ $-64$ $128$ ${\frac {968}{3}}$ ${\frac {136}{3}}$ $-1024$ $-{\frac {5440}{3}}$ $-{\frac {928}{3}}$ $-224$ ${\frac {2048}{3}}$ $2048$ ${\frac {15488}{3}}$ ${\frac {2176}{3}}$ ${\frac {156422}{15}}$ ${\frac {5912}{15}}$ ${\frac {170888}{45}}$ ${\frac {730}{9}}$ ${\frac {7142}{15}}$

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.