HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Parametrizing elliptic curves by modular units

François Brunault 1
1 Algèbre. Théorie des nombres
UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
Abstract : It is well-known that every elliptic curve over the rationals admits a parametrization by means of modular functions. In this short note, we show that only finitely many elliptic curves over Q can be parametrized by modular units. This answers a question raised by Zudilin in a recent work on Mahler measures. Further, we give the list of all elliptic curves E of conductor up to 1000 parametrized by modular units supported in the rational torsion subgroup of E. Finally, we raise several open questions.
Document type :
Journal articles
Complete list of metadata

Cited literature [10 references]  Display  Hide  Download

https://hal-ens-lyon.archives-ouvertes.fr/ensl-01400935
Contributor : François Brunault Connect in order to contact the contributor
Submitted on : Tuesday, November 22, 2016 - 4:23:46 PM
Last modification on : Tuesday, November 19, 2019 - 2:32:36 AM
Long-term archiving on: : Tuesday, March 21, 2017 - 12:24:58 AM

File

mod_units.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

François Brunault. Parametrizing elliptic curves by modular units. Journal of the Australian Mathematical Society, Cambridge University Press, 2016, 100, pp.33 - 41. ⟨10.1017/S1446788715000233⟩. ⟨ensl-01400935⟩

Share

Metrics

Record views

28

Files downloads

64