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ON A SPECIAL CASE OF WATKINS' CONJECTURE.
- Source :
-
Proceedings of the American Mathematical Society . Feb2018, Vol. 146 Issue 2, p541-545. 5p. - Publication Year :
- 2018
-
Abstract
- Watkins' conjecture asserts that for a rational elliptic curve E the degree of the modular parametrization is divisible by 2r, where r is the rank of E. In this paper, we prove that if the modular degree is odd, then E has rank zero. Moreover, we prove that the conjecture holds for all rank two rational elliptic curves of prime conductor and positive discriminant. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 146
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 126578646
- Full Text :
- https://doi.org/10.1090/proc/13759