{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T09:15:43Z","timestamp":1776849343638,"version":"3.51.2"},"reference-count":46,"publisher":"American Mathematical Society (AMS)","issue":"236","license":[{"start":{"date-parts":[[2002,5,11]],"date-time":"2002-05-11T00:00:00Z","timestamp":1021075200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>This paper provides empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus\u00a02 curves. The second of these conjectures relates six quantities associated to a Jacobian over the rational numbers. One of these six quantities is the size of the Shafarevich-Tate group. Unable to compute that, we computed the five other quantities and solved for the last one. In all 32\u00a0cases, the result is very close to an integer that is a power of\u00a02. In addition, this power of\u00a02 agrees with the size of the 2-torsion of the Shafarevich-Tate group, which we could compute.<\/p>","DOI":"10.1090\/s0025-5718-01-01320-5","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T22:13:53Z","timestamp":1027721633000},"page":"1675-1697","source":"Crossref","is-referenced-by-count":31,"title":["Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves"],"prefix":"10.1090","volume":"70","author":[{"given":"E.","family":"Flynn","sequence":"first","affiliation":[]},{"given":"Franck","family":"Lepr\u00e9vost","sequence":"additional","affiliation":[]},{"given":"Edward","family":"Schaefer","sequence":"additional","affiliation":[]},{"given":"William","family":"Stein","sequence":"additional","affiliation":[]},{"given":"Michael","family":"Stoll","sequence":"additional","affiliation":[]},{"given":"Joseph","family":"Wetherell","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2001,5,11]]},"reference":[{"key":"1","unstructured":"[AS1] A. 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