On a special case of Watkins’ conjecture
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 rati...
Guardado en:
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2017
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v146_n2_p541_Kazalicki http://hdl.handle.net/20.500.12110/paper_00029939_v146_n2_p541_Kazalicki |
| Aporte de: |
| Sumario: | 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. © 2017 American Mathematical Society. |
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