Kirti Joshi

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math.NT2025

On the analytic rank of the twin prime elliptic curve $y^{2} = x (x - 2) (x - p)$

Kirti Joshi

Let $p \geq 7$ and suppose $(p, p - 2)$ are twin prime numbers, in [Hatley, 2009], the elliptic curve $E_{p} : y^{2} = x (x - 2) (x - p)$ was considered in the context of a conjecture by Jason Beers…

math.NT2017

On the equation $N_{p_{1}} (E) \cdot N_{p_{2}} (E) \dots N_{p_{k}} (E) = n$

Kirti Joshi

For a given elliptic curve $E / Q$ , let $N_{p} (E)$ be the number of points on $E$ modulo $p$ for a prime of good reduction for $E$ . Given integer $n$ , let $G_{k} (E, n)$ be the nu…

On the analytic rank of the twin prime elliptic curve y2=x(x−2)(x−p)

On the equation Np1​​(E)⋅Np2​​(E)⋯Npk​​(E)=n

On the analytic rank of the twin prime elliptic curve $y^{2} = x (x - 2) (x - p)$

On the equation $N_{p_{1}} (E) \cdot N_{p_{2}} (E) \dots N_{p_{k}} (E) = n$