Equation 677 Database

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Magma 98cfe7aeb626…

magma 98cfe7aeb626
Size
529
Isomorphism class hash
98cfe7aeb6265785fd08fe2e37a1b96f3d5c4af13f721fc249ed17ddf3944bd9
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Submitted by
dwrensha
Submitted at
2026-05-16 12:58:34
Display reorder
528,524,188,140,284,116,236,308,428,24,8,164,380,476,452,212,92,500,332,68,356,404,260,296,525,143,382,243,297,150,255,434,317,48,220,132,352,251,302,409,106,319,181,210,425,283,440,228,189,496,239,395,526,446,387,73,441,38,246,463,399,277,98,306,461,89,192,427,316,392,50,505,141,413,202,27,144,415,478,268,229,339,16,258,393,448,521,34,347,379,351,398,104,390,372,127,285,63,160,421,383,30,59,450,190,125,110,21,51,288,217,91,105,460,346,368,323,369,41,120,117,374,222,234,244,215,481,327,497,204,454,178,506,355,424,315,391,389,56,483,194,324,169,402,237,57,77,112,298,185,335,342,240,491,79,523,142,495,412,62,373,128,312,474,87,370,75,83,309,484,45,5,151,129,134,407,396,115,149,445,414,29,214,184,36,286,54,3,516,42,1,329,429,195,207,432,256,313,85,23,47,37,338,124,203,490,114,488,511,64,146,94,137,121,364,294,25,325,443,509,435,475,250,276,447,287,354,494,28,489,512,471,467,161,513,300,349,118,12,274,9,170,518,499,318,88,378,459,388,55,311,53,145,416,65,253,14,422,472,292,437,375,417,502,165,403,282,439,49,371,40,168,74,2,363,11,200,479,147,486,290,384,468,155,265,223,66,187,381,238,201,159,221,76,44,206,442,517,281,248,361,269,95,271,172,31,162,304,102,235,254,386,477,58,480,334,133,84,249,377,39,43,0,527,456,230,138,71,19,60,514,7,219,245,15,109,453,78,148,337,353,310,362,280,247,464,330,226,419,340,122,465,263,451,301,97,520,216,423,411,213,113,487,470,252,485,270,70,344,400,430,457,198,17,365,331,180,191,350,345,367,482,473,4,93,299,291,154,303,46,96,272,157,278,196,231,358,259,295,227,504,126,119,401,82,328,293,273,501,186,385,108,410,6,152,173,175,99,208,139,242,394,26,420,233,111,13,431,508,498,438,158,333,336,469,153,107,320,130,32,321,307,433,72,267,449,326,341,406,22,275,458,167,205,376,279,69,343,156,174,176,182,135,163,131,462,257,20,177,522,444,123,493,52,10,199,360,455,418,197,357,241,266,224,100,211,408,305,33,90,314,61,183,35,510,466,225,289,171,18,262,179,503,232,405,492,80,67,209,426,397,103,322,193,86,515,136,348,436,264,101,218,519,366,81,507,166,359,261 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 + α, b = 14 + 9α. Here β = 14 + 9α 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