Equation 677 Database

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Size 65

222 isomorphism classes.

magma 5e80e1c2 of size 65 magma b8dd5d8f of size 65 magma b841b444 of size 65 magma 3e7f7877 of size 65 magma f6a46900 of size 65 magma 22cb8afe of size 65 magma 17d8eb76 of size 65 magma a09c4223 of size 65 magma 62917c53 of size 65 magma d8ba33b5 of size 65 magma 86e94818 of size 65 magma eff27734 of size 65 magma 4d60c34f of size 65 magma bcf3ee89 of size 65 magma 84076266 of size 65 magma 2db4eae0 of size 65 magma 3a1e3dea of size 65 magma a9f62e24 of size 65 magma 3180ad8d of size 65 magma f8838644 of size 65 magma cce41c1f of size 65 magma e9460cea of size 65 magma 65891b0f of size 65 magma b25ea767 of size 65 magma fdf5f382 of size 65 magma adb39c7b of size 65 magma c8b00e8b of size 65 magma fb895e25 of size 65 magma 4f5c5308 of size 65 magma d368fcff of size 65 magma fba993da of size 65 magma 200706f0 of size 65 magma 31b39e99 of size 65 magma a687d51f of size 65 magma d283ee66 of size 65 magma 11540e60 of size 65 magma 82788998 of size 65 magma b24873ef of size 65 magma b2f3cd20 of size 65 magma 4ddcb373 of size 65 magma 954a2425 of size 65 magma 47b26c2e of size 65 magma 4f47b623 of size 65 magma 9741437d of size 65 magma 70fbce4d of size 65 magma 58acf36c of size 65 magma c633edfa of size 65 magma b307f9e7 of size 65 magma c93f5316 of size 65 magma 8819209a of size 65 magma 48d4131c of size 65 magma 2ec82192 of size 65 magma a6f8f14c of size 65 magma f4f72483 of size 65 magma aa12d1af of size 65 magma 003b1571 of size 65 magma 3f4c16e1 of size 65 magma 87aba77d of size 65 magma 33fc7ab4 of size 65 magma 41328e14 of size 65 magma 48377dac of size 65 magma 37e131d0 of size 65 magma b9c83ee2 of size 65 magma d999f02d of size 65 magma a3dbb2a8 of size 65 magma 5c1fa523 of size 65 magma dcedbe28 of size 65 magma c84e71ca of size 65 magma 5e8db79a of size 65 magma ad2693ca of size 65 magma 6da5e676 of size 65 magma 58222ccd of size 65 magma e0ddb86f of size 65 magma b356224f of size 65 magma 3519a427 of size 65 magma d3adc358 of size 65 magma e6bbf558 of size 65 magma e2a478bb of size 65 magma 055eb219 of size 65 magma 35abc553 of size 65 magma ef4a4f27 of size 65 magma 58666f80 of size 65 magma 1de75750 of size 65 magma 24594ade of size 65 magma be22598f of size 65 magma 555d8536 of size 65 magma fbd23cd9 of size 65 magma 3a4a4157 of size 65 magma 6997491d of size 65 magma 90fd6808 of size 65 magma 38a4e23a of size 65 magma 8513f427 of size 65 magma 5751a2f2 of size 65 magma 07e8f68f of size 65 magma dc2fe347 of size 65 magma 57f0a271 of size 65 magma d33e4a3e of size 65 magma 51b008b2 of size 65 magma f80d3e42 of size 65 magma 458b3cfe of size 65 magma 58f4898e of size 65 magma 3c7860e7 of size 65 magma 14697465 of size 65 magma 3866b47a of size 65 magma f1e2c600 of size 65 magma fd86fc29 of size 65 magma a08efb26 of size 65 magma 9a5b7058 of size 65 magma 3f658a46 of size 65 magma cc21ed90 of size 65 magma 198f8683 of size 65 magma 368900d3 of size 65 magma 25532901 of size 65 magma 62fadf6a of size 65 magma bc5f623c of size 65 magma 3233330d of size 65 magma 06e28404 of size 65 magma eb741fb6 of size 65 magma b82bea23 of size 65 magma 299bf89d of size 65 magma f3708aca of size 65 magma 8ecda3bf of size 65 magma 0c204955 of size 65 magma df8d5557 of size 65 magma 5aa74a2d of size 65 magma 34f20f8c of size 65 magma 7b4d8683 of size 65 magma 02a5eb7a of size 65 magma 101de34e of size 65 magma 73fd8288 of size 65 magma 33430dad of size 65 magma 5a6f57af of size 65 magma 9c565a9f of size 65 magma 357eb5a0 of size 65 magma 676093fc of size 65 magma 19ea6a14 of size 65 magma e6ff3ea7 of size 65 magma 4af6d9f6 of size 65 magma f6b6fc56 of size 65 magma 4dbd6b00 of size 65 magma 7b2d22e1 of size 65 magma 96b025db of size 65 magma 8782a898 of size 65 magma 5b838974 of size 65 magma 9dc1b756 of size 65 magma b88a5e69 of size 65 magma a559a3ae of size 65 magma 0f0ec421 of size 65 magma 61e4460e of size 65 magma 7662547f of size 65 magma 7bddf6e5 of size 65 magma c2d2ffbf of size 65 magma 0898d182 of size 65 magma bf96e953 of size 65 magma 62d5cd00 of size 65 magma b87a4471 of size 65 magma 1c6b3e96 of size 65 magma dd5d8cb2 of size 65 magma ebc786cb of size 65 magma b7ef46c5 of size 65 magma cd941b7d of size 65 magma 7d1a9ea3 of size 65 magma 7eb365a4 of size 65 magma c683f2f4 of size 65 magma 69e303b0 of size 65 magma 58758ff0 of size 65 magma 6086f007 of size 65 magma fd865ad8 of size 65 magma e051b0f3 of size 65 magma 520f0c8b of size 65 magma 164604ba of size 65 magma 0d8cdfde of size 65 magma 96615941 of size 65 magma e3fb6778 of size 65 magma dc3952d3 of size 65 magma cb0e3d6c of size 65 magma d958d834 of size 65 magma ba7c5b5f of size 65 magma 0afaa5a9 of size 65 magma cb899e6f of size 65 magma 1d08ed48 of size 65 magma bef86252 of size 65 magma edd74923 of size 65 magma 616ee92b of size 65 magma c6bb22b6 of size 65 magma 59c0dab3 of size 65 magma d5c298f3 of size 65 magma 15e0002a of size 65 magma 05c0aaa7 of size 65 magma 01253a2a of size 65 magma 9017e525 of size 65 magma 8cce333a of size 65 magma 8e5759f6 of size 65 magma 9f23da99 of size 65 magma b8eeccb6 of size 65 magma 65ec2d14 of size 65 magma c6a86994 of size 65 magma e1d7ea9e of size 65 magma 789271f8 of size 65 magma 3d491508 of size 65 magma 2e8e4ac0 of size 65 magma b42b2593 of size 65 magma 40ac4fa0 of size 65 magma 6b720d89 of size 65 magma 49acd73e of size 65 magma 82fe7354 of size 65 magma a72914db of size 65 magma ea8bb884 of size 65 magma 2fbfbc69 of size 65 magma 514dffc0 of size 65 magma 24d4369d of size 65 magma b3dac6ff of size 65 magma a96a88e4 of size 65 magma bc84586c of size 65 magma 2c9cca33 of size 65 magma 5779f8ce of size 65 magma 34588157 of size 65 magma ba8e767a of size 65 magma 96138771 of size 65 magma 6f4d58a1 of size 65 magma b0c577ef of size 65 magma 2ab683a2 of size 65

Commentary

Permutation-twisted 5x13 fibre bundles (size 65 = 5 x 13). In June 2026 I submitted ~198 new size-65 magmas of one construction type, a 5x13 generalisation of the size-35 "switched fibre product" family of magma#ed4c392b. Coordinates (i,u) with i in F_5, u in F_13. The quotient by the 5-class congruence is the F_5 affine magma magma#e549b5f8 (i*j = 2i+4j); each 13-element fibre carries the F_13 affine law magma#babb8d44 (u*v = 9u+11v). The operation is (i,u)*(j,v) = (2i+4j, 9u+11v) if i=j (i,u)*(j,v) = (2i+4j, p^-1(9 p(u)+11 p(v))) if i!=j where p is a FIXED but ARBITRARY permutation of the F_13 FIBRE -- i.e. a bijection of the 13 fibre values {0,...,12}, an element of S_13 -- applied identically on every off-diagonal fibre. (p permutes the 13 layers within a fibre, not the 5 fibres and not the 65 elements.) Key fact: every such permutation p yields a valid Latin eq677 magma that also satisfies eq255. This is verified EXHAUSTIVELY for the F_7 fibre (all 7! = 5040 permutations are valid); for F_11/F_13/F_19 it is not exhaustive (13! is ~6 billion) but every one of several thousand random permutations passed. When p is affine (e.g. the identity) the twisted off-diagonal law is itself affine and one recovers a previously known affine bundle; a non-affine p gives a genuinely new isomorphism class. Distinct p almost never give isomorphic magmas, so this one recipe produces an essentially unbounded number of size-65 classes: 200 random permutations gave 200 distinct classes, 199 new to the DB. I submitted ~198 representatives; the family is not exhausted. All are right-cancellative and non-idempotent. Each diagonal fibre is a submagma isomorphic to magma#babb8d44; the quotient is magma#e549b5f8. A worked example with explicit coordinates is magma#b25ea767. The same recipe works at every size P*Q with P in {5,11} a valid eq677 base and Q in {5,7,11,13,19} a fibre prime carrying an affine eq677 law (sizes 25,35,55,65,77,95 < 100; F_9/F_16 fibres reach 45/80/99). See sizes 55 and 95 for the F_5 x F_11 and F_5 x F_19 analogues. [text written by Claude]

last edited by dwrensha at 2026-06-17 12:17:34 · history