Hyperelliptic modular curves X₀*(N) with square-free levels

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1. [1] A. O. L. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann. 185 (1970), 134-160. 
2. [2] A. O. L. Atkin and D. J. Tingley, Numerical tables on elliptic curves, in: Modular Functions of One Variable IV, B. Birch and W. Kuyk (eds.), Lecture Notes in Math. 476, Springer, Berlin, 1975, 74-144. 
3. [3] P. Deligne et M. Rapoport, Les schémas de modules de courbes elliptiques, in: Modular Functions of One Variable II, P. Deligne and W. Kuyk (eds.), Lecture Notes in Math. 349, Springer, Berlin, 1973, 143-316. Zbl0281.14010
4. [4] M. Eichler, The basis problem for modular forms and the traces of the Hecke operators, in: Modular Functions of One Variable I, W. Kuyk (ed.), Lecture Notes in Math. 320, Springer, Berlin, 1973, 75-151. 
5. [5] R. Hartshorne, Algebraic Geometry, Grad. Texts in Math. 52, Springer, New York, 1977. 
6. [6] Y. Hasegawa, Table of quotient curves of modular curves X₀(N) with genus 2, Proc. Japan Acad. Ser. A 71 (1995), 235-239. Zbl0873.11040
7. [7] K. Hashimoto, On Brandt matrices of Eichler orders, Mem. School Sci. Engrg. Waseda Univ. 59 (1995), 143-165. 
8. [8] H. Hijikata, Explicit formula of the traces of Hecke operators for Γ₀(N), J. Math. Soc. Japan 26 (1974), 56-82. Zbl0266.12009
9. [9] J. Igusa, Kroneckerian model of fields of elliptic modular functions, Amer. J. Math. 81 (1959), 561-577. Zbl0093.04502
10. [10] P. G. Kluit, Hecke operators on Γ*(N) and their traces , Dissertation of Vrije Universiteit, Amsterdam, 1979. 
11. [11] J. Lehner and M. Newman, Weierstrass points of Γ₀(N), Ann. of Math. 79 (1964), 360-368. Zbl0124.29203
12. [12] N. Murabayashi, On normal forms of modular curves of genus 2, Osaka J. Math. 29 (1992), 405-418. Zbl0774.14025
13. [13] A. P. Ogg, Hyperelliptic modular curves, Bull. Soc. Math. France 102 (1974), 449-462. Zbl0314.10018
14. [14] A. P. Ogg, Modular functions, in: The Santa Cruz Conference on Finite Groups, B. Cooperstein and G. Mason (eds.), Proc. Sympos. Pure Math. 37, Amer. Math. Soc., Providence, R.I., 1980, 521-532. 
15. [15] A. Pizer, An algorithm for computing modular forms on Γ₀(N), J. Algebra 64 (1980), 340-390. Zbl0433.10012
16. [16] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Iwanami Shoten and Princeton Univ. Press, 1971. Zbl0221.10029
17. [17] M. Yamauchi, On the traces of Hecke operators for a normalizer of Γ₀(N), J. Math. Kyoto Univ. 13 (1973), 403-411. Zbl0267.10038