2017 Fiscal Year Final Research Report
On the modularity of elliptic curves and modular forms from a viewpoint of computational number theory
| Project/Area Number |
15K17515
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | 楕円曲線 / モジュラー形式 / 高速計算 |
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| Outline of Final Research Achievements |
According to this research project, we provided some fast implementation to compute several family of elliptic curves over algebraic number field, and elliptic modular forms with associated Hecke algebra. More precisely, we achieved to get two efficient algorithm: (i) Searching all elliptic curves having everywhere good reduction with given conductor, and (ii) Calculating maximal orders of Hecke algebra with prescribed ramification of primes over the rational field. In addition, using several refinements by this project, we get an implementation of pairings (from elliptic curves) at the high security bit levels.
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| Free Research Field |
計算機数論
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