dc.contributor.author |
Miret, Josep M. (Josep Maria) |
dc.contributor.author |
Moreno Chiral, Ramiro |
dc.contributor.author |
Rio, Anna |
dc.date |
2012-01-25T11:57:51Z |
dc.date |
2012-01-25T11:57:51Z |
dc.date |
2007 |
dc.identifier |
0214-1493 |
dc.identifier |
http://hdl.handle.net/10459.1/44519 |
dc.identifier |
https://doi.org/10.5565/PUBLMAT_PJTN05_07 |
dc.identifier.uri |
http://hdl.handle.net/10459.1/44519 |
dc.description |
Given an elliptic curve E and a finite subgroup G, V ́lu’s formulae concern to a separable isogeny IG : E → E ′ with kernel G. In particular, for a point P ∈ E these formulae express the first elementary symmetric polynomial on the abscissas of the points in the set P + G as the difference between the abscissa of IG (P ) and the first elementary symmetric polynomial on the abscissas of the nontrivial points of the kernel G. On the other hand, they express Weierstraß coefficients of E ′ as polynomials in the coefficients of E and two additional parameters: w0 = t and w1 = w. We generalize this by defining parameters wn for all n ≥ 0 and giving analogous formulae for all the elementary symmetric polynomials and the power sums on the abscissas of the points in P +G. Simultaneously, we obtain an efficient way of performing computations
concerning the isogeny when G is a rational group. |
dc.language |
eng |
dc.publisher |
Universitat Autònoma de Barcelona. Departament de Matemàtiques |
dc.relation |
Reproducció del document publicat a https://doi.org/10.5565/PUBLMAT_PJTN05_07 |
dc.relation |
Reproducció del document publicat a http://ddd.uab.cat/record/52?ln=ca |
dc.relation |
Publicacions matemàtiques, 2007, vol. Extra, p. 147–163 |
dc.rights |
(c) Universitat Autònoma de Barcelona. Departament de Matemàtiques, 2007 |
dc.rights |
info:eu-repo/semantics/openAccess |
dc.subject |
Elliptic curve |
dc.subject |
Isogeny |
dc.subject |
Rational subgroup |
dc.subject |
Corbes el·líptiques |
dc.subject |
Nombres, Teoria dels |
dc.subject |
Anàlisi diofàntica |
dc.title |
Generalization of Vélu’s formulae for isogenies between elliptic curves |
dc.type |
article |
dc.type |
publishedVersion |