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Label Description Gaussian rational numbers First cubic field First cyclic cubic field
3.1.503.1 Non-monogenic field First quartic field First cyclic quartic field First biquadratic field First $S_4$ field
4.0.3136.1 First $A_4$ field
5.1.1609.1 First quintic field
5.1.2209.1 First $D_5$ field
5.5.14641.1 First cyclic quintic field
5.1.18496.1 First $A_5$ field
5.1.35152.1 First $F_5$ field
6.0.9747.1 First sextic field
14.2.20325604337285010030592.1 Nonsolvable field ramified at 2 and 13
17.1.604462909807314587353088.1 Harbater number field
18.2.4768875488962616064464333777.1 Field associated with 17-torsion on an elliptic curve
18.2.40254497110927943179349807054456171205137.1 Nonsolvable field ramified at only 17
20.2.558854584859141340505879659895771.1 The 19-division field for CM elliptic curve for $\Q(\sqrt{-7})$
20.2.206007596521214410095208558252435839890349094339.1 Field associated with 19-torsion on an elliptic curve