A note on basic Iwasawa λ-invariants of imaginary quadratic fields and congruence of modular forms
Indivisibility of class numbers of imaginary quadratic function fields
Ranks of quadratic twists of an elliptic curve
Imaginary quadratic fields whose Iwasawa λ-invariant is equal to 1
Indivisibility of special values of Dedekind zeta functions of real quadratic fields
A note on class number 1 criteria for totally real algebraic number fields
Optimal curves differing by a 3-isogeny
Stein and Watkins conjectured that for a certain family of elliptic curves E, the X₀(N)-optimal curve and the X₁(N)-optimal curve of the isogeny class 𝓒 containing E of conductor N differ by a 3-isogeny. In this paper, we show that this conjecture is true.
Optimal curves differing by a 5-isogeny
For i = 0,1, let be the -optimal curve of an isogeny class of elliptic curves defined over ℚ of conductor N. Stein and Watkins conjectured that E₀ and E₁ differ by a 5-isogeny if and only if E₀ = X₀(11) and E₁ = X₁(11). In this paper, we show that this conjecture is true if N is square-free and is not divisible by 5. On the other hand, Hadano conjectured that for an elliptic curve E defined over ℚ with a rational point P of order 5, the 5-isogenous curve E’ := E/⟨P⟩ has a rational point of order...
Mollin's conjecture
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