On the Classification of Lattices Over <svg      style="vertical-align:-3.06pt;width:75px;" id="M1" height="24.4125" version="1.1" viewBox="0 0 75 24.4125" width="75"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
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</svg> Which Are Even Unimodular <svg     style="vertical-align:-0.0pt;width:16.875px;" id="M2" height="15.25" version="1.1" viewBox="0 0 16.875 15.25" width="16.875"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
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</svg>-Lattices of Rank 32

<div class="floats-full-page floats-full-page-other"><h2>Table 3</h2><div class="floats-full-page-caption">The lattices of rank 12.</div><div class="floats-full-page-content"><table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr /></td></tr><tr class="thead"><td align="left">no.</td><td align="center"><span style="width: 11.075px;"><svg height="11.3125" id="M104" style="vertical-align:-0.1092pt" version="1.1" viewbox="0 0 11.075 11.3125" width="11.075" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path d="M627 18l-10 -26q-79 6 -116 27t-69 76q-41 71 -71 138q-13 29 -27.5 39t-42.5 10h-46l-27 -145q-13 -74 -2.5 -88.5t78.5 -20.5l-6 -28h-271l5 28q66 6 82.5 21.5t30.5 87.5l71 387q12 66 2 78.5t-77 19.5l8 28h233q102 0 147 -29q65 -43 65 -129q0 -69 -45.5 -117&#10;t-115.5 -72q40 -86 66 -133q39 -68 65 -101q28 -37 73 -51zM491 483q0 67 -33.5 101t-91.5 34q-35 0 -51 -10q-13 -8 -20 -48l-45 -245h49q71 0 113 28q79 52 79 140z" id="x1D445"></path></g>
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<g transform="matrix(.017,-0,0,-.017,.062,10.462)"><path d="M624 398l-8 -50h-120l-40 -185h112l-8 -50h-115l-52 -239h-59l51 239h-148l-52 -239h-59l53 239h-126l9 50h128l41 185h-121l8 50h124l47 214h59l-48 -214h149l46 214h59l-47 -214h117zM439 348h-148l-40 -185h147z" id="x23"></path></g>
</svg>Aut</td><td align="center"><span style="width: 39.712502px;"><svg height="17.4125" id="M106" style="vertical-align:-4.39398pt" version="1.1" viewbox="0 0 39.712502 17.4125" width="39.712502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,18.475,15.95)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5&#10;q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g><g transform="matrix(.012,-0,0,-.012,24.186,15.95)"><path d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" id="x2C"></path></g><g transform="matrix(.012,-0,0,-.012,26.899,15.95)"><path d="M983 225q0 -112 -67 -174.5t-150 -62.5q-91 0 -154.5 43.5t-113.5 129.5q-49 -85 -104 -129t-138 -44q-98 0 -158.5 66t-60.5 154q0 59 21 106.5t54.5 75.5t70.5 43t73 15q90 0 152.5 -43.5t112.5 -128.5q48 84 104.5 128t140.5 44q93 0 155 -65t62 -158zM478 196&#10;q-27 49 -47 80t-50 67t-64 54t-73 18q-48 0 -81.5 -47t-33.5 -128q0 -96 37.5 -157.5t99.5 -61.5q68 0 117.5 47t94.5 128zM889 204q0 91 -35.5 151t-99.5 60q-68 0 -119 -47t-95 -127q27 -49 47 -80.5t50 -67.5t65 -54t74 -18q113 0 113 183z" id="x221E"></path></g>
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</svg></span></td></tr><tr><td class="thead-hr" colspan="5"><hr /></td></tr><tr><td align="left">1</td><td align="center">3<svg height="15.4" id="M108" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 17.200001 15.4" width="17.200001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></td><td align="center">22568879259648000</td><td align="center">2</td><td align="center">3<svg height="15.4" id="M109" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 17.200001 15.4" width="17.200001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></td></tr><tr><td align="left">2</td><td align="center">4<svg height="15.4" id="M110" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 17.200001 15.4" width="17.200001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></td><td align="center">8463329722368</td><td align="center">1</td><td align="center"> </td></tr><tr><td align="left">3</td><td align="center">6<svg height="15.25" id="M111" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 20.112499 15.25" width="20.112499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></td><td align="center">206391214080</td><td align="center">1</td><td align="center"><svg height="15.4" id="M112" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 16.1625 15.4" width="16.1625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>(<svg height="19.375" id="M113" style="vertical-align:-2.78459pt" version="1.1" viewbox="0 0 20.450001 19.375" width="20.450001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,15.85)"><path d="M769 521v-16q-67 -12 -67 -95q-1 -26 17 -68l36.5 -89.5t17.5 -87.5q0 -69 -75 -129t-148 -60q-66 0 -114 22v-202h-117v235q-24 21 -56 21q-72 0 -114 -75l-20 9q18 64 52 110q43 58 117 58q16 0 21 -1v250q0 139 -30 197q-33 64 -83 64q-29 -1 -48 -20t-19 -46&#10;t12 -47.5t28.5 -34l33.5 -27.5t29 -36.5t12 -53.5q0 -51 -50 -99q-49 -47 -116 -64l-9 22q23 7 50 34q49 53 7 109q-16 23 -39 41q-57 43 -57 99q0 71 53 112q54 42 133 42q62 0 111.5 -24t74.5 -66h2q40 88 143 88q87 0 117 -56q6 -10 17 -34t18.5 -37.5t23 -27t36.5 -17.5&#10;zM695 503v2q-41 4 -67 20.5t-36 37t-17 40.5t-20.5 33.5t-36.5 13.5q-32 0 -52 -24q-30 -37 -30 -112v-379q18 -13 43 -45q27 -34 48 -50t47 -16q38 0 65.5 24.5t27.5 71.5q0 34 -41 114t-41 130q0 41 29 78.5t81 60.5z" id="x1D513"></path></g>
<g transform="matrix(.012,-0,0,-.012,14.05,7.688)"><path d="M137 343l67 33q37 17 63 17q79 0 129.5 -53t50.5 -131q0 -92 -58 -156.5t-147 -64.5t-147 68t-58 182q0 63 17 119t43 95.5t61.5 72t69 52t67.5 31.5q62 22 128 33l6 -32q-56 -11 -108 -35q-149 -71 -184 -231zM227 337q-47 0 -95 -27q-6 -23 -6 -70q0 -93 36 -155.5&#10;t96 -62.5q53 0 78 45.5t25 105.5q0 68 -35 116t-99 48z" id="x36"></path></g>
</svg>)</td></tr><tr><td align="left">4</td><td align="center">12<svg height="15.5375" id="M114" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 18.924999 15.5375" width="18.924999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.4)"><path d="M716 28l-8 -28h-254l8 28q55 5 66 17.5t5 47.5l-30 145h-232l-74 -138q-21 -43 -11 -54.5t72 -17.5l-6 -28h-235l8 28q53 7 73.5 21t53.5 70l319 540l33 8q6 -43 33 -176l80 -381q10 -49 26.5 -63t72.5 -19zM495 281l-49 264h-2l-149 -264h200z" id="x1D434"></path></g>
<g transform="matrix(.012,-0,0,-.012,12.525,15.475)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg></td><td align="center">101016305280</td><td align="center">1</td><td align="center"> </td></tr><tr><td align="left">5</td><td align="center"><span style="width: 13.975px;"><svg height="11.7625" id="M115" style="vertical-align:-0.4095pt" version="1.1" viewbox="0 0 13.975 11.7625" width="13.975" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></span></td><td align="center">2690072985600</td><td align="center">1</td><td align="center"><span style="width: 23.8375px;"><svg height="15.5125" id="M116" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 23.8375 15.5125" width="23.8375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.363)"><path d="M671 0h-247v28q49 7 60 18.5t0 45.5l-155 438h-2q-21 -61 -74 -204.5t-75 -210.5q-15 -51 -4.5 -65t67.5 -22v-28h-221v28q50 9 69 26.5t45 84.5l202 517l32 9l194 -535q23 -61 42 -78.5t67 -23.5v-28z" id="x39B"></path></g>
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</svg></span></td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr" /></td></tr></table></td></tr></table></div></div>

Table 3 | On the Classification of Lattices Over <svg      style="vertical-align:-3.06pt;width:75px;" id="M1" height="24.4125" version="1.1" viewBox="0 0 75 24.4125" width="75"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,-0,0,-.022,26.138,16.937)"><path id="x221A" d="M782 703l-309 -950l-231 505l-91 -47l-18 35l147 78l194 -431h2l264 810h42z" /></g><g transform="matrix(.022,-0,0,-.022,.062,20.538)"><path id="x211A" d="M794 -138l-9 -21q-74 -1 -142 15q-79 19 -254 130q-139 7 -231 87q-52 44 -83 107t-31 135q0 145 103 247.5t274 102.5q145 0 249.5 -93.5t104.5 -240.5q0 -126 -73 -212.5t-179 -116.5q137 -85 271 -140zM673 302q0 152 -78 239.5t-201 87.5q-50 0 -84.5 -74t-34.5 -209
q0 -265 118 -317l66 18l31 -19q76 19 129.5 90t53.5 184zM298 54q-66 94 -66 292q0 178 50 256q-62 -32 -99 -98t-37 -162q0 -98 41 -174t111 -114z" /></g><g transform="matrix(.022,-0,0,-.022,18.377,20.538)"><path id="x28" d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" /></g>

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			<g transform="matrix(.022,-0,0,-.022,43.262,20.538)"><path id="x2212" d="M535 230h-483v50h483v-50z" /></g><g transform="matrix(.022,-0,0,-.022,56.421,20.538)"><path id="x33" d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" /></g><g transform="matrix(.022,-0,0,-.022,67.181,20.538)"><path id="x29" d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" /></g>

		
	
</svg> Which Are Even Unimodular <svg     style="vertical-align:-0.0pt;width:16.875px;" id="M2" height="15.25" version="1.1" viewBox="0 0 16.875 15.25" width="16.875"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,-0,0,-.022,.062,15.187)"><path id="x2124" d="M734 170q-25 -130 -36 -170h-661l-8 15l420 599h-173q-77 0 -102 -7t-39 -29q-19 -29 -35 -87l-29 1l12 183h24q9 -16 19 -20.5t34 -4.5h543l7 -14l-416 -598l166 -2q94 0 131.5 7.5t58.5 29.5q28 29 55 103zM639 614h-89l-397 -567l88 -7z" /></g>

		
	
</svg>-Lattices of Rank 32

title

Table 3: On the Classification of Lattices Over <svg      style="vertical-align:-3.06pt;width:75px;" id="M1" height="24.4125" version="1.1" viewBox="0 0 75 24.4125" width="75"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,-0,0,-.022,26.138,16.937)"><path id="x221A" d="M782 703l-309 -950l-231 505l-91 -47l-18 35l147 78l194 -431h2l264 810h42z" /></g><g transform="matrix(.022,-0,0,-.022,.062,20.538)"><path id="x211A" d="M794 -138l-9 -21q-74 -1 -142 15q-79 19 -254 130q-139 7 -231 87q-52 44 -83 107t-31 135q0 145 103 247.5t274 102.5q145 0 249.5 -93.5t104.5 -240.5q0 -126 -73 -212.5t-179 -116.5q137 -85 271 -140zM673 302q0 152 -78 239.5t-201 87.5q-50 0 -84.5 -74t-34.5 -209
q0 -265 118 -317l66 18l31 -19q76 19 129.5 90t53.5 184zM298 54q-66 94 -66 292q0 178 50 256q-62 -32 -99 -98t-37 -162q0 -98 41 -174t111 -114z" /></g><g transform="matrix(.022,-0,0,-.022,18.377,20.538)"><path id="x28" d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" /></g>

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			<g transform="matrix(.022,-0,0,-.022,43.262,20.538)"><path id="x2212" d="M535 230h-483v50h483v-50z" /></g><g transform="matrix(.022,-0,0,-.022,56.421,20.538)"><path id="x33" d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" /></g><g transform="matrix(.022,-0,0,-.022,67.181,20.538)"><path id="x29" d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" /></g>

		
	
</svg> Which Are Even Unimodular <svg     style="vertical-align:-0.0pt;width:16.875px;" id="M2" height="15.25" version="1.1" viewBox="0 0 16.875 15.25" width="16.875"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,-0,0,-.022,.062,15.187)"><path id="x2124" d="M734 170q-25 -130 -36 -170h-661l-8 15l420 599h-173q-77 0 -102 -7t-39 -29q-19 -29 -35 -87l-29 1l12 183h24q9 -16 19 -20.5t34 -4.5h543l7 -14l-416 -598l166 -2q94 0 131.5 7.5t58.5 29.5q28 29 55 103zM639 614h-89l-397 -567l88 -7z" /></g>

		
	
</svg>-Lattices of Rank 32

description

Table 3 | On the Classification of Lattices Over 
	
		
			

			
				
			
			

		
	
 Which Are Even Unimodular 
	
		
			

		
	
-Lattices of Rank 32

Table 3

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International Journal of Mathematics and Mathematical Sciences

On the Classification of Lattices Over Which Are Even Unimodular -Lattices of Rank 32

Table 3