Algorithmic Number Theory: 7th International Symposium, by Nigel Boston, Harris Nover (auth.), Florian Hess, Sebastian

By Nigel Boston, Harris Nover (auth.), Florian Hess, Sebastian Pauli, Michael Pohst (eds.)

This publication constitutes the refereed court cases of the seventh foreign Algorithmic quantity idea Symposium, ANTS 2006, held in Berlin, Germany in July 2006.

The 37 revised complete papers awarded including four invited papers have been conscientiously reviewed and chosen for inclusion within the ebook. The papers are equipped in topical sections on algebraic quantity idea, analytic and ordinary quantity thought, lattices, curves and forms over fields of attribute 0, curves over finite fields and functions, and discrete logarithms.

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Math. Soc. ) 23 (1990), no. 2, 375–382. 5. J. E. Cremona, Modular symbols for Γ1 (N ) and elliptic curves with everywhere good reduction, Math. Proc. Cambridge Philos. , 111 (1992) no. 2, 199–218. 6. J. E. Cremona, Algorithms for modular elliptic curves, Cambridge University Press, 1992. 7. J. E. Cremona, Algorithms for modular elliptic curves (2nd edition), Cambridge University Press, 1997. uk/personal/jec/book/fulltext/. 8. J. E. Cremona, Computing the degree of the modular parametrization of a modular elliptic curve, Math.

The Elliptic Curve Database for Conductors to 130000 27 Table 5. 8 # |X| # 37074 11512 4013 1954 426 468 250 85 52 73 20 19 142 152 162 172 192 202 212 232 262 9 2 6 4 2 3 2 4 1 all > 1 55979 The Manin Constant Recall that the Manin constant for an elliptic curve E of conductor N is the rational number c such that ϕ∗ (ωE ) = c(2πif (z)dz), where ωE is a N´eron differential on E, f is the normalized newform for Γ0 (N ) associated to E, and ϕ : X0 (N ) → E is the modular parametrization. A longstanding conjecture is that c = 1 for all elliptic curves over Q which are optimal quotients of J0 (N ) (or “strong Weil curves” in the older terminology).

E. uk/personal/jec/ftp/data/. 10. J. E. uk/personal/jec/mwrank/. 11. J. E. Cremona and S. Siksek, Computing a Lower Bound for the Canonical Height on Elliptic Curves over Q, ANTS VII Proceedings 2006, Springer 2006. 12. W. Duke, Elliptic curves with no exceptional primes, C. R. Acad. Sci. Paris S´er. I Math. 325 (1997), no. 8, 813–818. 13. B. Edixhoven , On the Manin constants of modular elliptic curves, in Arithmetic algebraic geometry (Texel, 1989), Progr. Math. 89, Birkh¨ auser, Boston (1991), 25–39.

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