Class Group of $\mathbb{Q}(\sqrt{-47})$ Calculate the group of $\mathbb{Q}(\sqrt{-47})$.
I have this: The Minkowski bound is $4,36$ approximately.
Thanks!

@potato, the chip way to do this is binary forms, certainly for negative discriminants. The result is five classes, an odd number which therefore guarantees that the principal genus ("squares") contains everything. Then I threw in $\mathbb Q(\sqrt {-479})$ because it goes slightly past the online table.
Note that the original computer they gave me was named phoebus, which refers to Apollo. When that broke, they tried to call it phoebusjunior but the spelling came out a bit off.
jagy@phobeusjunior:~/old drive/home/jagy/Cplusplus$ ./classGroup
Absolute value of discriminant? 
47
  class  number  5

 all  
( 1, 1, 12)
( 2, -1, 6)
( 2, 1, 6)
( 3, -1, 4)
( 3, 1, 4)

 squares  
( 1, 1, 12)
( 2, -1, 6)
( 2, 1, 6)
( 3, -1, 4)
( 3, 1, 4)

Discriminant        -47     h :    5     Squares :    5     

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jagy@phobeusjunior:~/old drive/home/jagy/Cplusplus$ ./classGroup
Absolute value of discriminant? 
479
  class  number  25

 all  
( 1, 1, 120)
( 2, -1, 60)
( 2, 1, 60)
( 3, -1, 40)
( 3, 1, 40)
( 4, -1, 30)
( 4, 1, 30)
( 5, -1, 24)
( 5, 1, 24)
( 6, -5, 21)
( 6, -1, 20)
( 6, 1, 20)
( 6, 5, 21)
( 7, -5, 18)
( 7, 5, 18)
( 8, -1, 15)
( 8, 1, 15)
( 9, -5, 14)
( 9, 5, 14)
( 10, -9, 14)
( 10, -1, 12)
( 10, 1, 12)
( 10, 9, 14)
( 11, -7, 12)
( 11, 7, 12)



Discriminant       -479     h :   25     Squares :   25     Fourths :   25
jagy@phobeusjunior:~/old drive/home/jagy/Cplusplus$ 
    jagy@phobeusjunior:~/old drive/home/jagy/Cplusplus$ 

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