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2002 The Splitting of Primes in Division Fields of Elliptic Curves
W. Duke, Á. Tóth
Experiment. Math. 11(4): 555-565 (2002).


We give a global description of the Frobenius for the division fields of an elliptic curve E that is strictly analogous to the cyclotomic case. This is then applied to determine the splitting of a prime p in a subfield of such a division field. These subfields include a large class of nonsolvable quintic extensions and our application provides an arithmetic counterpart to Klein's "solution" of quintic equations using elliptic functions. A central role is played by the discriminant of the ring of endomorphisms of the reduced curve modulo p.


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W. Duke. Á. Tóth. "The Splitting of Primes in Division Fields of Elliptic Curves." Experiment. Math. 11 (4) 555 - 565, 2002.


Published: 2002
First available in Project Euclid: 10 July 2003

zbMATH: 1162.11348
MathSciNet: MR1969646

Primary: 11G , 11G05 , 11R , 11R32

Keywords: division fields , Elliptic curves , quintic expressions

Rights: Copyright © 2002 A K Peters, Ltd.


Vol.11 • No. 4 • 2002
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