منابع مشابه
Hasse Invariants for the Clausen Elliptic Curves
Gauss’s 2F1 ( 1 2 1 2 1 | x ) hypergeometric function gives periods of elliptic curves in Legendre normal form. Certain truncations of this hypergeometric function give the Hasse invariants for these curves. Here we study another form, which we call the Clausen form, and we prove that certain truncations of 3F2 ( 1 2 1 2 1 2 1 1 | x ) and 2F1 ( 1 4 3 4 1 | x ) in Fp[x] are related to the charac...
متن کاملOn Invariants of Elliptic Curves on Average
Abstract. We prove several results regarding some invariants of elliptic curves on average over the family of all elliptic curves inside a box of sides A and B. As an example, let E be an elliptic curve defined over Q and p be a prime of good reduction for E. Let eE (p) be the exponent of the group of rational points of the reduction modulo p of E over the finite field Fp. Let C be the family o...
متن کاملThe Odderon and Invariants of Elliptic Curves. *
In this talk we present some links of the theory of the odderon with elliptic curves. These results were obtained in an earlier work [19]. The natural degrees of freedom of the odderon turn out to coincide with conformal invariants of elliptic curves with a fixed ‘sign’. This leads to a formulation of the odderon which is modular invariant with respect to Γ — the unique normal subgroup of SL(2,...
متن کاملOn the asymptotics for invariants of elliptic curves modulo p
Let E be an elliptic curve defined over Q. Let E(Fp) denote the elliptic curve modulo p. It is known that there exist integers i p and f p such that E(Fp) ∼= Z/ i pZ × Z/ i p f pZ. We study questions related to i p and f p . In particular, for any α > 0 and k ∈ N, we prove there exist positive constants cα and ck such that for any A > 0 ∑ p≤x (log i p) α = cα li(x) + O ( x (log x)A ) and ∑ p≤x ...
متن کاملOn the rank of certain parametrized elliptic curves
In this paper the family of elliptic curves over Q given by the equation Ep :Y2 = (X - p)3 + X3 + (X + p)3 where p is a prime number, is studied. Itis shown that the maximal rank of the elliptic curves is at most 3 and someconditions under which we have rank(Ep(Q)) = 0 or rank(Ep(Q)) = 1 orrank(Ep(Q))≥2 are given.
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ژورنال
عنوان ژورنال: Kyushu Journal of Mathematics
سال: 1994
ISSN: 1340-6116
DOI: 10.2206/kyushujm.48.307