Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Rank-one Drinfel'd modules on elliptic curves


Authors: D. S. Dummit and David Hayes
Journal: Math. Comp. 62 (1994), 875-883
MSC: Primary 11G09; Secondary 11G15
MathSciNet review: 1218342
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The sgn-normalized rank-one Drinfeld modules $ \phi $ associated with all elliptic curves E over $ {\mathbb{F}_q}$ for $ 4 \leq q \leq 13$ are computed in explicit form. (Such $ \phi $ for $ q < 4$ were computed previously.) These computations verify a conjecture of Dorman on the norm of $ j(\phi ) = {a^{q + 1}}$ and also suggest some interesting new properties of $ \phi $. We prove Dorman's conjecture in the ramified case. We also prove the formula $ \deg N(a) = q({h_k} - 1 + q)$, where $ N(a)$ is the norm of a and $ {h_k}$ is the class number of $ k = {\mathbb{F}_q}(E)$. We describe a remarkable conjectural property of the trace of a in even characteristic that holds in all the examples.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11G09, 11G15

Retrieve articles in all journals with MSC: 11G09, 11G15


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1994-1218342-4
PII: S 0025-5718(1994)1218342-4
Article copyright: © Copyright 1994 American Mathematical Society