Equation 677 Database

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Magma 33778629f1dd…

magma 33778629f1dd
Size
387
Isomorphism class hash
33778629f1ddc8ad85e51cb97d2f1523eed8c600519e3d7b42d49feb1a83e6d2
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Submitted by
omegaestable
Submitted at
2026-07-22 04:26:12
Display reorder
358,332,304,141,127,318,113,290,155,347,238,266,103,89,224,75,252,61,346,60,88,265,251,102,237,74,223,373,6,34,211,197,48,183,20,169,338,108,80,257,243,94,229,66,271,364,216,188,25,11,202,53,174,39,369,30,2,179,221,16,207,44,193,386,385,384,383,378,382,379,380,381,376,200,172,9,51,186,37,214,23,371,46,18,195,181,32,167,4,209,345,278,250,87,73,264,59,236,101,366,176,204,41,27,218,13,190,55,339,230,258,95,81,272,67,244,109,340,68,96,273,259,110,245,82,231,351,162,134,311,297,148,283,120,325,375,22,50,171,213,8,199,36,185,354,300,328,165,151,286,137,314,123,348,76,104,225,267,62,253,90,239,372,168,196,33,19,210,5,182,47,349,254,226,63,105,240,91,268,77,350,324,296,133,119,310,161,282,147,360,292,320,157,143,334,129,306,115,362,308,280,117,159,294,145,322,131,370,208,180,17,3,194,45,222,31,352,284,312,149,135,326,121,298,163,363,146,118,295,281,132,323,160,309,336,270,242,79,65,256,107,228,93,343,262,234,71,57,248,99,276,85,374,184,212,49,35,170,21,198,7,367,14,42,219,205,56,191,28,177,337,92,64,241,227,78,269,106,255,344,100,72,249,235,86,277,58,263,356,316,288,125,1,302,153,330,139,359,114,142,319,305,156,291,128,333,377,38,10,187,173,24,215,52,201,355,138,166,287,329,124,315,152,301,353,122,150,327,313,164,299,136,285,357,154,126,303,289,140,331,335,317,342,84,112,233,275,70,261,98,247,365,54,26,203,189,40,175,12,217,341,246,274,111,97,232,83,260,69,361,130,158,279,321,116,307,144,293,368,192,220,0,43,178,29,206,15 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

It is the Cartesian product of two affine E677 magmas. On F_43, define x * y = 36x + 14y + 1 mod 43. On F_3^2, define r * s = r + As, where A = [[0,1],[1,1]]. The full operation on F_43 x F_3^2 is therefore (x,r) diamond (y,s) = (36x + 14y + 1, r + As). The magma has 43 x 9 = 387 elements. For the scalar component, E677 reduces to the three congruences ab(1+b^2) = 1, a + b^2(a^2+b) = 0, b^2(a+1) + b + 1 = 0. For a = 36 and b = 14 modulo 43, one has b^2 = 24, and direct substitution gives 36 x 14 x 25 = 1 mod 43, 36 + 24(36^2 + 14) = 0 mod 43, 24 x 37 + 14 + 1 = 0 mod 43.

last edited by omegaestable at 2026-07-22 04:28:27 · history