✦ LIBER ✦

Potential Good Reduction of Elliptic Curves

✍ Scribed by Masanari Kida

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 239 KB
Volume: 34
Category: Article
ISSN: 0747-7171
DOI: 10.1006/jsco.2002.0555

No coin nor oath required. For personal study only.

✦ Synopsis

We show that there is no elliptic curve defined over the field of rational numbers that attains good reduction at every finite place under quadratic base change. We also give some examples of elliptic curves that acquire good reduction everywhere under cubic or quartic base changes.

📜 SIMILAR VOLUMES

Nonexistence of Elliptic Curves with Goo

Nonexistence of Elliptic Curves with Good Reduction Everywhere over Real Quadratic Fields

✍ Masanari Kida; Takaaki Kagawa 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 302 KB

Twists and Reduction of an Elliptic Curv

Twists and Reduction of an Elliptic Curve

✍ S. Comalada 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 404 KB

Degrees of Parametrizations of Elliptic

Degrees of Parametrizations of Elliptic Curves by Shimura Curves

✍ Shuzo Takahashi 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 146 KB

In this paper, we study some properties of parametrizations of elliptic curves by Shimura curves. Fix a square-free positive integer N and an isogeny class E of elliptic curves of conductor N defined over Q. Consider a pair (D, M ) such that N=DM and the number of prime factors of D is even. Let J b

False Division Towers of Elliptic Curves

✍ David E Rohrlich 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 229 KB

Indivisible Points on Families of Ellipt

Indivisible Points on Families of Elliptic Curves

✍ Rajiv Gupta; Keith Ramsay 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 376 KB

In this paper we consider families of elliptic curves E n over Q arising as twists. Given rational points P n on E n , we ask how often P n is indivisible in the group of rational points of E n , as n varies over the positive integers. We prove, following the method of Silverman for families with no

Exponents of Class Groups and Elliptic C

Exponents of Class Groups and Elliptic Curves

✍ Siman Wong 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 102 KB

We show that the number of elliptic curves over Q with conductor N is < < = N 1Â4+= , and for almost all positive integers N, this can be improved to < < = N = . The second estimate follows from a theorem of Davenpart and Heilbronn on the average size of the 3-class groups of quadratic fields. The f