Rational points on the modular curves X split ( p )

Fumiyuki Momose

Compositio Mathematica (1984)

  • Volume: 52, Issue: 1, page 115-137
  • ISSN: 0010-437X

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Momose, Fumiyuki. "Rational points on the modular curves $X_{\mathrm {split}}(p)$." Compositio Mathematica 52.1 (1984): 115-137. <http://eudml.org/doc/89649>.

@article{Momose1984,
author = {Momose, Fumiyuki},
journal = {Compositio Mathematica},
keywords = {split Cartan structure; p-division points; non-cuspidal rational points; modular curves; C M point},
language = {eng},
number = {1},
pages = {115-137},
publisher = {Martinus Nijhoff Publishers},
title = {Rational points on the modular curves $X_\{\mathrm \{split\}\}(p)$},
url = {http://eudml.org/doc/89649},
volume = {52},
year = {1984},
}

TY - JOUR
AU - Momose, Fumiyuki
TI - Rational points on the modular curves $X_{\mathrm {split}}(p)$
JO - Compositio Mathematica
PY - 1984
PB - Martinus Nijhoff Publishers
VL - 52
IS - 1
SP - 115
EP - 137
LA - eng
KW - split Cartan structure; p-division points; non-cuspidal rational points; modular curves; C M point
UR - http://eudml.org/doc/89649
ER -

References

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  2. [2] B.G. Berkovic: Rational points on the jacobians of modular curves. Math. USSR Sbornik30 (4) (1976) 478-500. Zbl0385.14007
  3. [3] P. Deligne and M. Rapoport: Schémas de modules des courbes elliptiques. Vol. II of the Proceedings of the International Summer School on modular functions, Antwerp (1972). Lecture Notes in Math. 349. Berlin- Heidelberg-New York: Springer1973. Zbl0281.14010MR337993
  4. [4] M.W. Kenku: The modular curve X0(39) and rational isogeny. Math. Proc. Cambridge Philos. Soc.85 (1979) 21-23. Zbl0392.14011MR510395
  5. [5] M.A. Kenku: The modular curves X0(65) and X0(91) and rational isogeny. Math. Proc. Cambridge Philos. Soc.87 (1980) 15-20. Zbl0479.14014MR549292
  6. [6] M.A. Kenku: The modular curve X0(169) and rational isogeny. J. London Math. Soc. (2) 22 (1980) 239-244. Zbl0437.14022MR588271
  7. [7] M.A. Kenku: On the modular curves X0(125), X 1(25) and X1(49). J. London Math. Soc. (2) 23 (1981) 415-427. Zbl0425.14006MR616546
  8. [8] S. Lang: Elliptic functions. Reading, Mass.: Addison-Wesley. Zbl0316.14001MR409362
  9. [9] B. Mazur: Rational points on modular curves. Proceedings of a conference on modular functions held in Bonn 1976. Lecture Notes in Math. 601. Berlin-Heidelberg-New York: Springer1977. Zbl0357.14005MR450283
  10. [10] B. Mazur: Modular curves and the Eisenstein ideal. Publ. Math. I.H.E.S.47 (1977). Zbl0394.14008
  11. [11] B. Mazur: Rational isogenies of prime degree. Inv. Math.44 (1978) 129-162. Zbl0386.14009MR482230
  12. [12] B. Mazur and H.P.F. Swinnerton-Dyer: Arithmetic of Weil curves. Inv. Math.25 (1974) 1-61. Zbl0281.14016MR354674
  13. [13] J.F. Mestre: Points rationnels de la courbe modulaire X 0(169). Ann. Inst. Fourier, Grenoble 30-2 (1980) 17-27. Zbl0432.14017MR584269
  14. [14] A Ogg: Über die Automorphismengruppe von X0(N). Math. Ann.228 (1977) 279-292. Zbl0336.14002MR562500
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  18. [18] K. Ribet: Endomorphisms of semi-stable abelian varieties over number fields. Ann. Math.101 (1975) 555-562. Zbl0305.14016MR371903
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Citations in EuDML Documents

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  1. Takeshi Hibino, Naoki Murabayashi, Modular equations of hyperelliptic X₀(N) and an application
  2. Kenneth A. Ribet, On the equation a p + 2 α b p + c p = 0
  3. Yuri Bilu, Pierre Parent, Marusia Rebolledo, Rational points on X 0 + ( p r )
  4. Keisuke Arai, On uniform lower bound of the Galois images associated to elliptic curves
  5. M. A. Kenku, Fumiyuki Momose, Automorphism groups of the modular curves X 0 ( N )
  6. Loïc Merel, Arithmetic of elliptic curves and diophantine equations

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