Add to ORKGWe count by height the number of elliptic curves over the rationals, both up to isomorphism over the rationals and over an algebraic closure thereof, that admit a cyclic isogeny of degree $7$.Comment: 31 page
We outline PARI programs which assist with various algorithms related to descent via isogeny on elli...
We give asymptotics for the number of isomorphism classes of elliptic curves over arbitrary number f...
Building on Mazur's 1978 work on prime degree isogenies, Kenku determined in 1981 all possible cycli...
Let $n>1$ be an integer such that $X_{0}\!\left( n\right) $ has genus $0$, and let $K$ be a field of...
Mazur's isogeny theorem states that if $p$ is a prime for which there exists an elliptic curve $E / ...
We show there exist polynomial bounds on torsion of elliptic curves which come from a fixed geometri...
We find the number of elliptic curves with a cyclic isogeny of degree n over various number fields b...
AbstractIt is shown that there are at most eight Q-isomorphism classes of elliptic curves in each Q-...
Fix an elliptic curve $E$ over a number field $F$ and an integer $n$ which is a power of $3$. We stu...
We show that if $E$ is an elliptic curve over $\mathbf{Q}$ with a $\mathbf{Q}$-rational isogeny of d...
We show that if $E$ is an elliptic curve over $\mathbf{Q}$ with a $\mathbf{Q}$-rational isogeny of d...
Harron and Snowden counted the number of elliptic curves over $\mathbb{Q}$ up to height $X$ with tor...
Let $K$ be a quadratic field which is not an imaginary quadratic field of class number one. We descr...
Using methods from analytic number theory, for m \u3e 5 and for m = 4, we obtain asymptotics with po...
Let $E$ be an elliptic curve over a number field $K$. If for almost all primes of $K$, the reduction...
We outline PARI programs which assist with various algorithms related to descent via isogeny on elli...
We give asymptotics for the number of isomorphism classes of elliptic curves over arbitrary number f...
Building on Mazur's 1978 work on prime degree isogenies, Kenku determined in 1981 all possible cycli...
Let $n>1$ be an integer such that $X_{0}\!\left( n\right) $ has genus $0$, and let $K$ be a field of...
Mazur's isogeny theorem states that if $p$ is a prime for which there exists an elliptic curve $E / ...
We show there exist polynomial bounds on torsion of elliptic curves which come from a fixed geometri...
We find the number of elliptic curves with a cyclic isogeny of degree n over various number fields b...
AbstractIt is shown that there are at most eight Q-isomorphism classes of elliptic curves in each Q-...
Fix an elliptic curve $E$ over a number field $F$ and an integer $n$ which is a power of $3$. We stu...
We show that if $E$ is an elliptic curve over $\mathbf{Q}$ with a $\mathbf{Q}$-rational isogeny of d...
We show that if $E$ is an elliptic curve over $\mathbf{Q}$ with a $\mathbf{Q}$-rational isogeny of d...
Harron and Snowden counted the number of elliptic curves over $\mathbb{Q}$ up to height $X$ with tor...
Let $K$ be a quadratic field which is not an imaginary quadratic field of class number one. We descr...
Using methods from analytic number theory, for m \u3e 5 and for m = 4, we obtain asymptotics with po...
Let $E$ be an elliptic curve over a number field $K$. If for almost all primes of $K$, the reduction...
We outline PARI programs which assist with various algorithms related to descent via isogeny on elli...
We give asymptotics for the number of isomorphism classes of elliptic curves over arbitrary number f...
Building on Mazur's 1978 work on prime degree isogenies, Kenku determined in 1981 all possible cycli...