Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8959489 | Journal of Number Theory | 2018 | 24 Pages |
Abstract
We prove an analogue of the Brauer-Siegel theorem for the Legendre elliptic curves over K=Fq(t). Namely, denoting by Ed the elliptic curve with model y2=x(x+1)(x+td) over K, we show that, for dââ ranging over the integers, one haslogâ¡(|СХ(Ed/K)|â
Reg(Ed/K))â¼logâ¡H(Ed/K)â¼logâ¡q2â
d. Here, H(Ed/K) denotes the exponential differential height of Ed, СХ(Ed/K) its Tate-Shafarevich group (which is known to be finite), and Reg(Ed/K) its Néron-Tate regulator.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Richard Griffon,