Equation 677 Database

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Magma e5f80c8c4d95…

magma e5f80c8c4d95
Size
763
Isomorphism class hash
e5f80c8c4d955b2e7ec45b7beb68e76c2524dddbceafff239128b7ea945117d6
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 762) what is this?
Submitted by
dwrensha
Submitted at
2026-09-27 18:51:16
Display reorder
505,65,473,27,211,695,465,506,96,353,260,638,686,335,447,111,432,123,151,728,339,440,577,364,186,217,721,526,503,109,758,241,238,681,543,299,626,494,203,134,708,334,457,170,568,243,141,724,575,521,101,483,255,562,726,387,293,61,370,31,556,707,610,500,97,480,44,602,648,343,522,622,54,36,618,673,546,377,68,471,121,236,732,600,375,163,411,87,279,710,545,436,165,472,51,268,733,346,518,642,631,30,292,701,527,301,22,413,264,283,753,398,456,89,359,117,284,743,530,305,636,433,58,216,683,330,554,62,588,52,209,736,541,519,95,496,49,281,691,756,313,13,479,39,142,696,392,509,72,613,59,226,702,570,315,79,593,127,272,723,408,300,561,423,240,136,661,547,460,557,356,6,278,739,405,446,601,487,187,273,700,463,438,616,481,42,234,741,396,380,23,583,16,232,730,336,510,167,427,41,205,722,397,453,183,493,190,269,684,635,459,180,474,50,144,664,338,309,171,488,251,225,663,536,376,172,347,26,148,688,331,512,94,362,201,553,657,590,516,114,578,37,270,747,394,451,169,360,759,156,652,404,441,80,627,245,287,725,615,511,104,429,126,131,697,595,574,160,352,261,143,748,321,312,74,484,43,229,752,533,609,166,348,258,215,716,385,520,161,621,115,207,704,406,444,21,491,249,237,660,585,599,19,422,57,288,714,325,443,110,424,250,222,650,391,523,157,641,11,228,662,399,452,82,5,55,152,698,386,296,103,367,32,233,694,551,455,86,637,202,290,751,539,507,552,485,14,267,671,580,439,158,373,247,220,706,537,757,67,1,257,210,693,630,317,175,495,7,289,711,327,569,69,475,15,572,742,529,306,81,563,192,155,717,382,445,107,560,29,607,718,525,303,93,603,265,271,738,625,374,112,617,259,213,668,389,294,24,0,129,596,676,320,513,176,426,196,212,687,322,295,100,415,244,274,754,645,634,106,412,252,221,685,467,515,63,430,239,139,715,544,461,20,431,47,224,669,640,508,178,372,35,285,649,383,589,182,365,128,208,750,550,319,98,428,33,760,745,470,302,88,476,10,133,682,393,614,177,355,198,566,737,400,594,571,419,25,149,689,565,498,66,497,262,214,699,559,458,606,425,48,146,755,605,310,159,420,9,231,679,620,304,91,4,242,137,656,468,584,597,53,191,291,678,324,502,90,361,193,138,727,340,316,162,416,647,633,703,337,297,99,478,119,266,653,328,311,77,354,40,230,672,329,449,102,482,12,286,670,549,437,173,646,263,586,654,542,579,113,417,46,135,735,326,462,761,490,122,145,667,401,629,71,434,246,611,674,532,504,567,492,253,591,740,344,454,60,477,125,276,749,395,307,92,358,124,227,712,323,450,84,371,17,153,746,345,624,18,363,8,147,655,466,314,75,2,120,582,720,464,524,179,435,195,280,659,538,499,76,351,184,132,734,341,644,632,357,56,140,731,403,378,181,486,199,154,705,531,442,108,3,200,218,719,407,639,174,410,45,206,690,555,308,587,414,38,576,675,342,448,73,349,197,204,762,388,381,83,366,254,628,729,332,318,612,409,28,282,744,390,298,592,573,188,223,665,402,564,164,489,248,150,651,535,558,105,608,194,219,677,548,604,64,418,189,623,680,540,619,85,369,118,130,713,469,379,581,598,116,275,666,333,501,168,368,34,277,709,528,517,70,421,185,643,692,534,514,78,350,256,235,658,384 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Monogenic cyclic-affine Eq677 magma of order 763. On Z/763, in construction labels, x*y = 263x + 134y + 1 (mod 763). Element 0 generates the whole magma; there are 648 generators and 1 idempotent element(s). For any element r, the generated submagma has size 763/gcd(763, (263+134-1)r+1). Both coefficients are units modulo 763, so this is a quasigroup (left- and right-cancellative); its fiber matrix is all ones. The affine Eq677 conditions are ab(1+b^2)=1, a+a^2*b^2+b^3=0, and (b^2(a+1)+b+1)c=0 modulo n. These hold for the displayed parameters. Independently checked all 582169 Eq677 instances, all 763 Eq255 instances, and full set closure from generator 0 directly in the saved table. This is not a counterexample to Eq677 => Eq255. Found while enumerating monogenic cyclic-affine models of orders below 1000, working upward in order. These are standard affine constructions, added to fill gaps in the database. Construction labels may differ from the server canonical labels. Computed with OpenAI Codex working with dwrensha, 2026-09-27.

last edited by dwrensha at 2026-09-27 18:51:16 · history