Abstract
Using the rank of the Mordell-Weil group $E(\mathbb {Q})$ of an elliptic curve $E$ over $\mathbb Q$, we give a lower bound of the class number of the number field $\mathbb {Q}(E[p^{n}])$ generated by $p^n$-division points of $E$ when the curve $E$ does not possess a $p$-adic point of order $p: E(\mathbb {Q}_p)[p]=0$.
Citation
Toshiro Hiranouchi. "Local torsion primes and the class numbers associated to an elliptic curve over $\mathbb Q$." Hiroshima Math. J. 49 (1) 117 - 127, March 2019. https://doi.org/10.32917/hmj/1554516039
Information