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We calculate explicitly the j-invariants of the elliptic curves corresponding to rational points on the modular curve X+ ns(11) by giving an expression defined over Q of the j-function in terms of the function field generators X and Y of the elliptic curve X+ ns(11). As a result we exhibit infinitely-many elliptic curves over Q with non-split mod 11 representations.

Elliptic curves with nonsplit mod $11$ representations