AbstractIt is shown that there are at most eight Q-isomorphism classes of elliptic curves in each Q-isogeny class
Building on Mazur's 1978 work on prime degree isogenies, Kenku determined in 1981 all possible cycli...
AbstractWe exhibit a genus-2 curve C defined over Q(T) which admits two independent morphisms to a r...
Let $E$ be an elliptic curve over a number field $K$. If for almost all primes of $K$, the reduction...
AbstractIt is shown that there are at most eight Q-isomorphism classes of elliptic curves in each Q-...
We find the number of elliptic curves with a cyclic isogeny of degree n over various number fields b...
Let $n>1$ be an integer such that $X_{0}\!\left( n\right) $ has genus $0$, and let $K$ be a field of...
It is well known that two elliptic curves are isogenous if and only if they have same number of rati...
We count by height the number of elliptic curves over the rationals, both up to isomorphism over the...
We show that if $E$ is an elliptic curve over $\mathbf{Q}$ with a $\mathbf{Q}$-rational isogeny of d...
Let $K$ be a quadratic field which is not an imaginary quadratic field of class number one. We descr...
We show that if $E$ is an elliptic curve over $\mathbf{Q}$ with a $\mathbf{Q}$-rational isogeny of d...
Mazur's isogeny theorem states that if $p$ is a prime for which there exists an elliptic curve $E / ...
AbstractFor a prime N we denote by X0(N)(K) the set of K-rational points on the modul curve of ellip...
We outline PARI programs which assist with various algorithms related to descent via isogeny on elli...
Let $K$ be a number field. For which primes $p$ does there exist an elliptic curve $E / K$ admitting...
Building on Mazur's 1978 work on prime degree isogenies, Kenku determined in 1981 all possible cycli...
AbstractWe exhibit a genus-2 curve C defined over Q(T) which admits two independent morphisms to a r...
Let $E$ be an elliptic curve over a number field $K$. If for almost all primes of $K$, the reduction...
AbstractIt is shown that there are at most eight Q-isomorphism classes of elliptic curves in each Q-...
We find the number of elliptic curves with a cyclic isogeny of degree n over various number fields b...
Let $n>1$ be an integer such that $X_{0}\!\left( n\right) $ has genus $0$, and let $K$ be a field of...
It is well known that two elliptic curves are isogenous if and only if they have same number of rati...
We count by height the number of elliptic curves over the rationals, both up to isomorphism over the...
We show that if $E$ is an elliptic curve over $\mathbf{Q}$ with a $\mathbf{Q}$-rational isogeny of d...
Let $K$ be a quadratic field which is not an imaginary quadratic field of class number one. We descr...
We show that if $E$ is an elliptic curve over $\mathbf{Q}$ with a $\mathbf{Q}$-rational isogeny of d...
Mazur's isogeny theorem states that if $p$ is a prime for which there exists an elliptic curve $E / ...
AbstractFor a prime N we denote by X0(N)(K) the set of K-rational points on the modul curve of ellip...
We outline PARI programs which assist with various algorithms related to descent via isogeny on elli...
Let $K$ be a number field. For which primes $p$ does there exist an elliptic curve $E / K$ admitting...
Building on Mazur's 1978 work on prime degree isogenies, Kenku determined in 1981 all possible cycli...
AbstractWe exhibit a genus-2 curve C defined over Q(T) which admits two independent morphisms to a r...
Let $E$ be an elliptic curve over a number field $K$. If for almost all primes of $K$, the reduction...
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