Epimorphic Euler Genera

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Below are listed the epimorphic Euler genera for various numbers of notes.

Eight notes

Rank two

Genus(3^3*11), Genus(13^3*5)

Rank three

Genus(3*11*13), Genus(5*11*13), Genus(3*5*11) (patent), Genus(3*7*11) (patent)

Nine notes

Rank one

Genus(11^9)

Rank two

Genus(3^2*5^2), Genus(3^2*13^2)

Genus(5^2*7^2), Genus(5^2*11^2),

Genus(7^2*13^2), Genus(11^2*13^2)

Ten notes

Rank one

Genus(5^9), Genus(13^9)

Rank two

Genus(3^4*5), Genus(3^4*11), Genus(3^4*13)

Genus(5^4*7), Genus(5^4*11)

Genus(7^4*5), Genus(7^4*11), Genus(7^4*13)

Genus(13^4*11)

Twelve notes

Rank one

Genus(3^11) (Pythagorean)

Rank two

Genus(3^5*11), Genus(3*7^5)

Genus(3^3*5^2) (Duodene)

Genus(3^2*13^3) (12f), Genus(3^3*13^2) (patent)

Rank three

Genus(3*5^2*7), Genus(3*5^2*11), Genus(3*7^2*11)

Genus(5^2*7*13) (12f), Genus(5^2*11*13) (12f), Genus(3*11*13^2) (patent)

Fourteen notes

Genus(3^6*7), Genus(13^6*5) (weakly; patent)

Fifteen notes

Genus(3^4*11^2), Genus(5^4*11^2)

Genus(5^2*7^4), Genus(5^2*11^4), Genus(5^2*13^4)

Sixteen notes

Rank one

Genus(5^15), Genus(7^15)

Rank two

Genus(5^7*7)

Eighteen notes

Rank two

Genus(5^2*13^5)

Rank three

Genus(5^2*7*13^2), Genus(5^2*11^2*13)

Twenty notes

Rank two

Genus(7^4*11^3), Genus(13^9*11)

Rank three

Genus(7^4*5*11), Genus(7^4*11*13)

Twenty-one notes

Rank one

Genus(7^20)

Rank two

Genus(3^6*7^2), Genus(7^6*5^2), Genus(13^6*5^2)

Twenty-two notes

Rank one

Genus(5^21)

Rank two

Genus(5^10*7), Genus(7^10*3), Genus(11^10*5), Genus(11^10*13)

Twenty-four notes

Rank one

Genus(11^23)

Rank two

Genus(3^11*7) (patent), Genus(3^11*11), Genus(3^11*13)

Genus(5^2*11^7), Genus(5^2*13^7)

Rank three

Genus(3^3*5^2*7) (patent), Genus(3^3*5^2*11), Genus(3^3*5^2*13)

Genus(3^2*7*13^3) (24d)

Rank four

Genus(3*5^2*7*13) (24d)

Twenty-five notes

Rank one

Genus(5^24)

Rank two

Genus(5^4*7^4)

Twenty-six notes

Rank one

Genus(7^25)

Rank two

Genus(7^12*5), Genus(11^12*3), Genus(11^12*7)

Twenty-seven notes

Rank one

Genus(13^26)

Rank two

Genus(5^2*13^8)

Rank three

Genus(5^2*11^2*13^2) (patent)

Twenty-eight notes

Rank one

Genus(5^27)

Rank two

Genus(5^3*13^6)