 | 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
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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
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