Epimorphic Euler genera
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)