scholarly journals A parametrized set of cyclic cubic fields with even class-number

1986 ◽  
Vol 22 (2) ◽  
pp. 246-248 ◽  
Author(s):  
H.J. Godwin
Keyword(s):  
Class Number ◽  
Cubic Fields ◽  
Cyclic Cubic Fields

scholarly journals Cyclic Cubic Fields of Given Conductor and Given Index

2006 ◽  
Vol 49 (3) ◽  
pp. 472-480 ◽  
Author(s):  
Alan K. Silvester ◽  
Blair K. Spearman ◽  
Kenneth S. Williams
Keyword(s):  
Cubic Fields ◽  
Cyclic Cubic Fields

AbstractThe number of cyclic cubic fields with a given conductor and a given index is determined.

scholarly journals A note on class-number one in pure cubic fields

1979 ◽  
Vol 33 (148) ◽  
pp. 1317-1317
Author(s):  
H. C. Williams ◽  
Daniel Shanks
Keyword(s):  
Class Number ◽  
Cubic Fields

scholarly journals Torsion of elliptic curves over cyclic cubic fields

2018 ◽  
Vol 88 (319) ◽  
pp. 2443-2459 ◽  
Author(s):  
Maarten Derickx ◽  
Filip Najman
Keyword(s):  
Elliptic Curves ◽  
Cubic Fields ◽  
Cyclic Cubic Fields

scholarly journals Congruence relations of Ankeny-Artin-Chowla type for pure cubic fields

1984 ◽  
Vol 96 ◽  
pp. 95-112 ◽  
Author(s):  
Hiroshi Ito
Keyword(s):  
Elliptic Curve ◽  
Class Number ◽  
Congruence Relation ◽  
Bernoulli Numbers ◽  
Quadratic Fields ◽  
Hurwitz Numbers ◽  
Real Quadratic Fields ◽  
Congruence Relations ◽  
Cubic Fields ◽  
Real Quadratic

Ankeny, Artin and Chowla [1] proved a congruence relation among the class number, the fundamental unit of real quadratic fields, and the Bernoulli numbers. Our aim of this paper is to prove similar congruence relations for pure cubic fields. For this purpose, we use the Hurwitz numbers associated with the elliptic curve defined by y2 = 4x3 — 1 instead of the Bernoulli numbers (§ 3).

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