Elliptic curves with non-integral j-invariant and non-trivial Hasse invariant

COUNTING TROPICAL ELLIPTIC PLANE CURVES WITH FIXED j-INVARIANT

In complex algebraic geometry, the problem of enumerating plane elliptic curves of given degree with fixed complex structure has been solved by R.Pandharipande [8] using Gromov-Witten theory. In this article we treat the tropical analogue of this problem, the determination of the number Etrop(d) of tropical elliptic plane curves of degree d and fixed “tropical j-invariant” interpolating an appr...

Torsion Groups of Elliptic Curves with Integral j-Invariant over Pure Cubic Fields

We determine all possible torsion groups of elliptic curves E with integral j-invariant over pure cubic number fields K. Except for the groups Z/22, Z/32 and Z/22 @ Z/22, there exist only finitely many curves E and pure cubic fields K such that E over K has a given torsion group E,, (K), and they are all calculated here. The curves E over K with torsion group E roOR( K) r Z/22 0 Z/22 have j-inv...

Has a Non - Trivial Invariant Subspace

In this paper, to solve the invariant subspace problem, contraction operators are classified into three classes ; (Case 1) completely nonunitary contractions with a non-trivial algebraic element, (Case 2) completely non-unitary contractions without a non-trivial algebraic element, or (Case 3) contractions which are not completely non-unitary. We know that every operator of (Case 3) has a non-tr...

Implementing the 4-dimensional GLV method on GLS elliptic curves with j-invariant 0

The Gallant-Lambert-Vanstone (GLV) method is a very efcient technique for accelerating point multiplication on elliptic curves with e ciently computable endomorphisms. Galbraith, Lin and Scott (J. Cryptol. 24(3), 446-469 (2010)) showed that point multiplication exploiting the 2-dimensional GLV method on a large class of curves over Fp2 was faster than the standard method on general elliptic cur...

Ranks of Elliptic Curves over Q(t) with Constant J-invariant