{"paper":{"title":"Explicit mock Heegner points and BSD formula on certain Mordell curves","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dipramit Majumdar, Somnath Jha, Sumita Gunri","submitted_at":"2026-07-29T11:14:28Z","abstract_excerpt":"For a natural number $a$, let $E_{2a}$ be the Mordell elliptic curve $X^3 +Y^3=2a$. We give an explicit construction of (mock) Heegner point on the Mordell curve $E_{2p}$ for a prime $p\\equiv 4 \\mod 9$ and $E_{2p^2}$ for a prime $p\\equiv 7 \\mod 9$, under the assumption that $2$ is not a cube modulo $p$. We also verify the explicit Gross-Zagier formula for these curves and go on to show that the BSD formula holds for these curves up to a $2$-adic unit. Using a result of Burungale-Flach, we show that the full BSD formula holds for the rank zero curve $E_{2p}$ for $p\\equiv 7 \\mod 9$ and $E_{2p^2}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26774","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.26774/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}