{"paper":{"title":"On the Arakelov theory of elliptic curves","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Robin de Jong","submitted_at":"2003-12-18T13:41:48Z","abstract_excerpt":"This note contains an elementary discussion of the Arakelov intersection theory of elliptic curves. The main new results are a projection formula for elliptic arithmetic surfaces and a formula for the \"energy\" of an isogeny between Riemann surfaces of genus 1. The latter formula provides an answer to a question originally posed by Szpiro."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0312359","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"}