Refined Kodaira classes and conductors of twisted elliptic curves / Browkin J., Davies D. - Warszawa: Institute of mathematics, Polish academy of sciences, 2009. - iii, 45 p. - Incl. bibl. ref. - (Dissertationes mathematicae; 463) - ISSN 0012-3862  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

I. Twists ....................................................... 5 1. Introduction ................................................. 5 1.1. Preliminaries ........................................... 5 1.2. Notation ................................................ 6 1.3. The reduced minimal model of a curve .................... 7 1.4. Some important lemmas ................................... 7 2. The case p = 2 and d = -1 .................................... 9 2.1. Table 2.1 ............................................... 9 2.2. Additional conditions .................................. 10 2.3. Table 2.2 .............................................. 18 2.4. Main Theorem ........................................... 18 3. The case p = 2 and d = 2 .................................... 19 3.1. Table 3.1 .............................................. 19 3.2. Lemmas ................................................. 19 3.3. Main Theorem ........................................... 27 4. The case p = 3 and d = -3 ................................... 27 4.1. Table 4.1 .............................................. 27 4.2. Additional conditions and comments ..................... 27 4.3. Main Theorem ........................................... 28 5. The case p > 3 .............................................. 29 6. Nonquadratic twists ......................................... 29 6.1. General remarks ........................................ 29 6.2. Quartic twists in the case p = 2 ....................... 30 6.3. Sextic twists in the case p = 2 ........................ 31 6.4. Quartic twists in the case p = 3 ....................... 32 6.5. Sextic twists in the case p = 3 ........................ 33 6.6. Quartic and sextic twists in the case p > 3 ............ 34 II. Conductors ................................................. 35 7. Observations concerning conductors .......................... 35 7.1. Which numbers are conductors? .......................... 35 7.2. Curves with conductors differing by a prime power ...... 36 8. Estimates of #Ј(N) and #Cond(X) ............................. 38 References ..................................................... 39 Tables ......................................................... 41