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Section: New Results

Number and function fields

The article [13] written by J. Brau and J. Nathan on “Elliptic curves with 2-torsion contained in the 3-torsion field” has been published. This article study the modular curve X'(6) of level 6 defined over whose -rational points correspond to j-invariants of elliptic curves E over for which (E[2]) is a subfield of (E[3]). The authors characterize the j-invariants of elliptic curves with this property by exhibiting an explicit model of X'(6). X'(6)() then gives an infinite family of examples of elliptic curves with non-abelian "entanglement fields," which is relevant to the systematic study of correction factors of various conjectural constants for elliptic curves over .