International audienceThere is a modular curve X'(6) of level 6 defined over Q whose Q-rational points correspond to j-invariants of elliptic curves E over Q for which Q(E[2]) is a subfield of Q(E[3]). In this note we characterize the j-invariants of elliptic curves with this property by exhibiting an explicit model of X'(6). Our motivation is two-fold: on the one hand, X'(6) belongs to the list of modular curves which parametrize non-Serre curves (and is not well-known), and on the other hand, X'(6)(Q) gives an infinite family of examples of elliptic curves with non-abelian "entanglement fields," which is relevant to the systematic study of correction factors of various conjectural constants for elliptic curves over Q
A Q-curve is an elliptic curve over a number field K which is geometrically isogenous to each of its...
Abstract. Let E be an elliptic curve over a ¯nite ¯eld K = Fq, and n 6= char(K) a prime. Then the ¯e...
Let E be an elliptic curve defined over Q. We study the relationship between the torsion subgroup E(...
International audienceThere is a modular curve X'(6) of level 6 defined over Q whose Q-rational poin...
Abstract. We calculate explicitly the j-invariants of the elliptic curves corresponding to rational ...
We present various published and unpublished results on elliptic curves. In particular, we focus on ...
AbstractWe determine all possible torsion groups of elliptic curves E with integral j-invariant over...
We prove that the family $\mathcal{I}_{F_0}$ of elliptic curves over number fields that are geometri...
The determination of which finite abelian groups can occur as the torsion subgroup of an elliptic cu...
Let $E$ be an elliptic curve defined over $\mathbb{Q}$. We investigate $E(K)_{\text{tors}}$ for vari...
In a previous paper ([10]), the author examined the possible tor-sions of an elliptic curve over the...
AbstractTextIn a previous paper Najman (in press) [9], the author examined the possible torsions of ...
An elliptic curve defined over a number field K => Q, where [K: Q] < oo, is an abelian variety...
This dissertation concerns the formulation of an explicit modified Szpirobconjecture and the classif...
Let p be a prime number, p ? 2,3 and Fp the finite field with p elements. An elliptic curve E over F...
A Q-curve is an elliptic curve over a number field K which is geometrically isogenous to each of its...
Abstract. Let E be an elliptic curve over a ¯nite ¯eld K = Fq, and n 6= char(K) a prime. Then the ¯e...
Let E be an elliptic curve defined over Q. We study the relationship between the torsion subgroup E(...
International audienceThere is a modular curve X'(6) of level 6 defined over Q whose Q-rational poin...
Abstract. We calculate explicitly the j-invariants of the elliptic curves corresponding to rational ...
We present various published and unpublished results on elliptic curves. In particular, we focus on ...
AbstractWe determine all possible torsion groups of elliptic curves E with integral j-invariant over...
We prove that the family $\mathcal{I}_{F_0}$ of elliptic curves over number fields that are geometri...
The determination of which finite abelian groups can occur as the torsion subgroup of an elliptic cu...
Let $E$ be an elliptic curve defined over $\mathbb{Q}$. We investigate $E(K)_{\text{tors}}$ for vari...
In a previous paper ([10]), the author examined the possible tor-sions of an elliptic curve over the...
AbstractTextIn a previous paper Najman (in press) [9], the author examined the possible torsions of ...
An elliptic curve defined over a number field K => Q, where [K: Q] < oo, is an abelian variety...
This dissertation concerns the formulation of an explicit modified Szpirobconjecture and the classif...
Let p be a prime number, p ? 2,3 and Fp the finite field with p elements. An elliptic curve E over F...
A Q-curve is an elliptic curve over a number field K which is geometrically isogenous to each of its...
Abstract. Let E be an elliptic curve over a ¯nite ¯eld K = Fq, and n 6= char(K) a prime. Then the ¯e...
Let E be an elliptic curve defined over Q. We study the relationship between the torsion subgroup E(...