Abstract
We extend the heuristic introduced by Conrey, Farmer, Keating, Rubinstein, and Snaith in order to formulate conjectures for the -moments of L-functions of elliptic curves twisted by cubic characters. We also apply the work of Keating and Snaith on the -moments of characteristic polynomials of unitary matrices to extend our conjecture to such that and . Our conjectures are then numerically tested for two families. A novelty of our conjectures is that cubic twists naturally lead us to consider the possibility .
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