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Results tagged with torsion
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user 5015
5
votes
Is there an elliptic curve over a number field with a point of order 64 and Mordell-Weil ran...
I am aiming to construct an elliptic curve $E$ over a number field $K$ with an $p^k$-torsion point in $E(K)$ but $E(K)$ has rank $0$. … We would have $H=\mathbb{Q}(\sqrt{-7})$, the rank of $E(H)$ is zero, and all $2$-torsion points are $H$-rational.
This relies on $E$ having complex multiplication. …
- 8,945
5
votes
Possible $p$-torsion subgroup of $E(\mathbb{Q}_p)$, and if there is a theorem to say which c...
For odd primes: If the reduction is good and the reduction has no $p$-torsion (not "anomalous" as it is called) then there are no $p$-torsion over $\mathbb{Q}_p$. … In the first case the point $(0,0)$ is a $5$-torsion point, while in the second there are no torsion points in $E_2(\mathbb{Q}_5)$. …
- 8,945