Equation 677 Database

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Magma 576a7341bbd6…

magma 576a7341bbd6
Size
529
Isomorphism class hash
576a7341bbd69c717e51bf63233e66700ce9868afc67dc42b05e376631098d15
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Submitted by
dwrensha
Submitted at
2026-05-16 12:58:27
Display reorder
528,524,476,470,494,467,488,497,512,482,485,473,506,518,515,479,464,521,500,461,503,509,491,214,48,168,117,402,301,82,188,339,22,243,480,469,221,403,107,315,358,196,65,371,317,407,232,487,66,239,186,421,69,125,420,267,319,376,100,148,140,17,357,389,40,269,261,425,498,226,351,327,60,34,370,180,255,142,129,492,11,414,481,383,313,233,329,94,415,419,134,119,250,118,505,166,18,158,257,35,138,375,439,341,87,58,77,287,438,213,285,443,271,516,394,223,412,310,8,252,57,116,91,380,489,177,324,197,326,478,126,367,348,416,230,411,139,31,244,432,369,499,279,335,12,331,52,251,388,281,198,112,207,433,160,437,81,152,510,71,29,253,216,344,161,397,441,442,21,519,290,378,169,274,80,141,508,446,61,38,121,288,90,260,202,105,70,10,523,95,184,305,36,456,176,231,209,303,53,1,156,289,393,468,457,346,359,238,154,245,363,75,275,273,504,106,6,23,427,46,426,431,382,493,146,192,395,131,201,325,241,149,430,278,328,496,26,78,204,385,9,366,68,434,109,248,332,429,507,157,195,49,276,229,266,14,373,122,236,495,37,137,316,132,63,422,386,145,330,418,484,258,354,97,417,183,262,150,450,130,387,225,517,451,297,178,353,455,30,99,283,170,4,462,203,89,340,47,299,208,309,16,162,190,474,0,365,215,76,401,101,333,42,352,237,111,59,463,295,311,527,182,205,292,234,98,362,159,179,526,349,398,459,13,460,56,39,73,471,306,308,108,396,212,187,235,392,379,424,501,360,322,189,428,20,270,242,264,143,423,3,272,151,128,490,43,103,72,220,227,123,321,88,5,28,413,475,174,113,307,136,345,323,486,54,409,408,364,194,377,249,211,62,104,477,185,114,404,193,400,240,79,165,314,355,218,19,298,45,368,312,466,336,399,256,64,172,444,263,449,381,334,93,511,293,164,291,144,522,347,124,83,24,219,41,277,445,217,361,483,304,410,318,246,405,320,110,25,120,374,406,342,171,2,224,191,51,199,472,85,259,86,167,452,448,127,296,200,280,350,514,447,44,525,96,175,222,147,337,67,27,294,384,265,465,458,228,302,7,356,390,50,173,181,133,343,286,300,453,92,102,454,153,206,33,520,247,440,284,338,32,163,391,282,74,436,254,502,513,210,55,372,155,115,268,435,84,135,15 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Linear magma over the extension field F_529 = F_23[α]/⟨α² − 5⟩. Operation: x ◇ y = a·x + b·y in F_529 with a = 11 + 22α, b = 20 + 8α. Here β = 20 + 8α is a root of Φ_2_5(x) = x⁴ + x³ + 2x² + 2x + 1 in F_529, and α_coef = -β³ - β - 1. This is Pace Nielsen's "Type 2" non-fully-idempotent linear 677 magma family. Note: 10 ∤ (23² − 1) = 528, so F_529 has no primitive 10th roots of unity → no Type-1 (translation-invariant fully-idempotent) linear 677 magma exists at this size. But Φ_2_5 has 4 roots in F_529 (forming 2 Galois-conjugate orbits under Frobenius), giving 2 distinct iso classes of Type-2 magmas at this size. F_529 is the proper degree-2 extension of F_23; do NOT confuse with the ring Z/529Z (which has zero divisors and is NOT a field). Size 529, not fully idempotent, right-cancellative. This iso class is one of the two known Eq 677 magmas at size 529 in the DB. [text written by Claude]

last edited by dwrensha at 2026-05-16 12:59:10 · history