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Twists and Reduction of an Elliptic Curve

✍ Scribed by S. Comalada


Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
404 KB
Volume
49
Category
Article
ISSN
0022-314X

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πŸ“œ SIMILAR VOLUMES


Potential Good Reduction of Elliptic Cur
✍ Masanari Kida πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 239 KB

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.

Mordell–Weil Ranks of Quadratic Twists o
✍ Gwynneth Coogan; Jorge JimenΓ©z-Urroz πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 146 KB

Motivated by a conjecture of Mazur, Kuwata and Wang proved that for elliptic curves E 1 and E 2 whose j-invariants are not simultaneously 0 or 1728, there exist infinitely many square-free integers d for which the rank of the Mordell-Weil group of the d-quadratic twists of E 1 and E 2 satisfy: rkΓ°E

A Twisted AdjointL-Value of an Elliptic
✍ Keiji Goto πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 360 KB

We shall show an explicit value of a twisted adjoint L-value L(1, Ad( f ) /) attached to f. Here f is a primitive elliptic cusp form of ``Haupt''-type and / a quadratic character. The calculation can be done by using the formula of L(1, Ad( f ) /) obtained by Hida. This value supports numerically a

Exponents of Class Groups and Elliptic C
✍ Siman Wong πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 102 KB

We show that the number of elliptic curves over Q with conductor N is < < = N 1Γ‚4+= , 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