Congruences of the elliptic type

the investigation of the relationship between type a and type b personalities and quality of translation

چکیده ندارد.

Congruences of models of elliptic curves

Let OK be a discrete valuation ring with field of fractions K and perfect residue field. Let E be an elliptic curve over K, let L/K be a finite Galois extension and let OL be the integral closure of OK in L. Denote by X ′ the minimal regular model of EL over OL. We show that the special fibers of the minimal Weierstrass model and the minimal regular model of E over OK are determined by the infi...

Reduction of CM Elliptic Curves and Modular Function Congruences

Congruences between Heegner Points and Quadratic Twists of Elliptic Curves

We establish a congruence formula between p-adic logarithms of Heegner points for two elliptic curves with the same mod p Galois representation. As a first application, we use the congruence formula when p = 2 to explicitly construct many quadratic twists of analytic rank zero (resp. one) for a wide class of elliptic curves E. We show that the number of twists of E up to twisting discriminant X...

Positive Definite Quadratic Forms, Elliptic Curves and Cubic Congruences

Let F (x, y) = ax + bxy + cy be a positive definite binary quadratic form with discriminant Δ whose base points lie on the line x = −1/m for an integer m ≥ 2, let p be a prime number and let Fp be a finite field. Let EF : y = ax + bx + cx be an elliptic curve over Fp and let CF : ax + bx + cx ≡ 0(mod p) be the cubic congruence corresponding to F . In this work we consider some properties of pos...