{"paper":{"title":"An unexpected trace relation of CM points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel Kohen","submitted_at":"2018-06-29T10:34:53Z","abstract_excerpt":"Let $E/\\mathbb{Q}$ be an elliptic curve of conductor $N=p^2M$ where $p$ is an odd prime not dividing $M$. Let $\\mathcal{O}_f$ be the order of conductor $f$ (relatively prime to $N$) in an imaginary quadratic field $K$ in which $p$ is inert and such that the sign of the functional equation of $E/K$ is $-1$. Associated to these data there is a Shimura curve of non-split Cartan level at $p$ and a CM point of conductor $f$ on it. We can also consider a CM point of conductor $pf$ on another Shimura curve, using a split Cartan level at $p$. These curves admit parametrizations to $E$ and taking the i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.11337","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}