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Introduction Item: Title: Acknowledgements Item: Title: 2. Modular elliptic curves and p-adic lattices Children: Item: Title: 2.1. Modular elliptic curves via cohomology Item: Title: 2.2. Construction of the p-adic lattice Item: Title: 3. Explicit methods and algorithms Children: Item: Title: 3.1. The rational Hecke eigenclass Item: Title: 3.2. The homology class Item: Title: 3.3. The cohomology class Item: Title: 3.4. The multiplicative pairing Item: Title: 4. Numerical computations Children: Item: Title: 4.1. Recovering the curve from the L-invariant Item: Title: 4.2. Numerical results Item: Title: 5. Discussion and further improvements Item: Title: References Item: Title: Appendix A. Tables Item: Title: Real quadratic fields Item: Title: Cubic totally real fields Item: Title: Imaginary quadratic fields Item: Title: Cubic ATR fields Item: Title: Quartic ATR fields Info: Title: Author: Subject: Keywords: Creator: LaTeX with hyperref package Producer: pdfTeX-1.40.13 CreationDate: Sun Jun 21 14:39:36 CEST 2015 ModDate: Sun Jun 21 14:39:36 CEST 2015 ID: 0x2fb6c7d614c1f588bb81c2887891c2e4, 0x2fb6c7d614c1f588bb81c2887891c2e4 Filters: FilterPipeline: FlateDecode Fonts: Type1: Font: BaseFont: QPTREA+CMSY7 FontSubset: true FirstChar: 0 LastChar: 106 FontDescriptor: FontName: QPTREA+CMSY7 Flags: Symbolic FontBBox: -15, -951, 1251, 782 FontFile: true Font: BaseFont: KJSSVB+MSBM7 FontSubset: true FirstChar: 45 LastChar: 90 FontDescriptor: FontName: KJSSVB+MSBM7 Flags: Symbolic FontBBox: -45, -504, 2613, 1004 FontFile: true Font: BaseFont: BHEIRJ+CMSY6 FontSubset: true FirstChar: 0 LastChar: 106 FontDescriptor: FontName: BHEIRJ+CMSY6 Flags: Symbolic FontBBox: -4, -948, 1329, 786 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