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Extensions of CM elliptic curves and orbit counting on the projective line.
- Source :
-
Research in Number Theory . 5/1/2017, Vol. 3 Issue 1, p1-13. 13p. - Publication Year :
- 2017
-
Abstract
- There are several formulas for the number of orbits of the projective line under the action of subgroups of $$\mathrm{GL}_2$$ . We give an interpretation of two such formulas in terms of the geometry of elliptic curves, and prove a more general formula for a large class of congruence subgroups of Bianchi groups. Our formula involves the number of walks on a certain graph called an isogeny volcano. Underlying our results is a complete description of the group of extensions of a pair of CM elliptic curves, as well as the group of extensions of a pair of lattices in a quadratic field. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 25220160
- Volume :
- 3
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Research in Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 122762400
- Full Text :
- https://doi.org/10.1007/s40993-017-0073-y