{"paper":{"title":"Computing modular correspondences for abelian varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Damien Robert (INRIA Lorraine - LORIA), David Lubicz (IRMAR), Jean-Charles Faug\\`ere (INRIA Rocquencourt)","submitted_at":"2009-10-24T17:34:54Z","abstract_excerpt":"The aim of this paper is to give a higher dimensional equivalent of the classical modular polynomials $\\Phi_\\ell(X,Y)$. If $j$ is the $j$-invariant associated to an elliptic curve $E_k$ over a field $k$ then the roots of $\\Phi_\\ell(j,X)$ correspond to the $j$-invariants of the curves which are $\\ell$-isogeneous to $E_k$. Denote by $X_0(N)$ the modular curve which parametrizes the set of elliptic curves together with a $N$-torsion subgroup. It is possible to interpret $\\Phi_\\ell(X,Y)$ as an equation cutting out the image of a certain modular correspondence $X_0(\\ell) \\to X_0(1) \\times X_0(1)$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.4668","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":""},"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"}