Shimura correspondence Hecke L-functions Galois representations Heegner points L-series Cartan curves Computational methods Consani-Scholten quintic Elliptic curves modularity Faltings-Serre-Livné method Generalized Equations Hensel lifting Hilbert modular form Interpolation L-series special values Local factors Modular forms Newton-Hensel lifting Prime number Quadratic twists Real twists Sparse polynomial interpolation Sparse polynomial interpolations Sturm bound Twisting epsilon factors p-Adic integers