# About some family of elliptic curves

Source: [About some family of elliptic curves](<https://www.sota2.com/research/paper/68fa4ef01e209131ce95f8e1>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T10:03:55.428Z

Authors: K.Bugajska

Published: 2010-12-12T17:03:12.000Z

## Abstract

We examine the moduli space E=T\* of complex tori T(t)=C/L(t) where L(t)=cost.n(t)Lt. We find that the Dedekind eta function furnishes a bridge between the euclidean and hyperbolic structures on T\*=C-L/L as well as between the doubly periodic Weierstrass function p on T\* and the theta function for the lattice E(8). The former one allows us to rewrite the Lame equation for the Bers embedding of T(1,1) in a new form. We show that L has natural decomposition into 8 sublattices (each equivalent to L) together with appropriate half-points and that this leads to some local functions and to a relation with E(8)

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1012.2559>)

[PDF](<https://arxiv.org/pdf/1012.2559.pdf>)