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Some Rank Records for Elliptic Curves with Prescribed Torsion Over Quadratic Fields Cover

Some Rank Records for Elliptic Curves with Prescribed Torsion Over Quadratic Fields

By: Filip Najman  
Open Access
|Dec 2014

References

  1. [1] W. Bosma, J. J. Cannon, C. Fieker, A. Steel (eds.), Handbook of Magma functions, Edition 2.18 (2012).
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  3. [3] J. Bosnian, P. Bruin, A. Dujella, F. Najman, Ranks of elliptic curves with prescribed torsion over number fields, Int. Math. Res. Not. IMRN, to appear.
  4. [4] A. Dujella, High rank elliptic curves with prescribed torsion, http://web. math.hr/~duje/tors/tors.html
  5. [5] A. Dujella, M. Jukić Bokun, On the rank of elliptic curves overQ(i) with torsion group Z4 ⊕ Z4, Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), 93-96.10.3792/pjaa.86.93
  6. [6] A. Dujella, F. Najman, Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization, Period. Math. Hungar. 65 (2012), 193-203.10.1007/s10998-012-8257-7
  7. [7] N. Elkies, j = 0, rank 15; also 3-rank 6 and 7 in real and imaginary quadratic fields, Number Theory Listserv posting, December 30, 2009, http://listserv.nodak.edu/cgi-bin/wa.exe?A2= ind0912&L=NMBRTHRY&F=&S=&P=14012
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  10. [10] M. Laska and M. Lorenz, Rational points on elliptic curves over Qin elementary abelian 2-extensions of Q, J. Reine Angew. Math. 355 (1985), 163-172.
  11. [11] F. P. Rabarison, Structure de torsion des courbes elliptiques sur les corps quadratiques, Acta Arith. 144 (2010), 17-52.10.4064/aa144-1-3
DOI: https://doi.org/10.2478/auom-2014-0017 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 215 - 219
Submitted on: Sep 1, 2013
Accepted on: Dec 1, 2013
Published on: Dec 10, 2014
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2014 Filip Najman, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.