scholarly journals On elliptic curves of prime power conductor over imaginary quadratic fields with class number 1

2018 ◽  
Vol 118 (5) ◽  
pp. 1245-1276
Author(s):  
John Cremona ◽  
Ariel Pacetti
Keyword(s):  
Elliptic Curves ◽  
Class Number ◽  
Prime Power ◽  
Quadratic Fields ◽  
Imaginary Quadratic Fields

scholarly journals NOTE ON THE DIVISIBILITY OF THE CLASS NUMBER OF CERTAIN IMAGINARY QUADRATIC FIELDS

2009 ◽  
Vol 51 (1) ◽  
pp. 187-191 ◽  
Author(s):  
YASUHIRO KISHI
Keyword(s):  
Class Number ◽  
Diophantine Equations ◽  
Quadratic Field ◽  
Imaginary Quadratic Field ◽  
Quadratic Fields ◽  
Imaginary Quadratic Fields ◽  
Positive Integers

AbstractWe prove that the class number of the imaginary quadratic field $\Q(\sqrt{2^{2k}-3^n})$ is divisible by n for any positive integers k and n with 22k < 3n, by using Y. Bugeaud and T. N. Shorey's result on Diophantine equations.

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