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Dec 15, 2013 at 16:07 comment added abx Similar, no. The point is that torsion points of order $>2$ are much harder to write down. I would be tempted to guess that such counterexamples do not exist for a generic curve, but that would probably be very hard to prove.
Dec 15, 2013 at 15:55 comment added ginevra86 Thank you for your answer. In your counterexample, both $g_1$ and $g_2$ have order $2$. Are there similar counterexamples in the case where $\Gamma$ contains no element of order $2$?
Dec 15, 2013 at 15:42 history answered abx CC BY-SA 3.0