{
  "id": 6258,
  "curve_key": "248844738466401616:-519634093110816173011065280",
  "ainvs": [
    "0",
    "1",
    "0",
    "-5184265384716700",
    "601428346779800627560944"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 123.03033425729619,
  "faltings_height": 8.308764437468222,
  "conductor": "14434156287109352275243676706300230118515304296",
  "bad_primes": [
    "2",
    "11",
    "29",
    "16737361",
    "8769846117254513",
    "3502991567478773401"
  ],
  "discriminant": "-147343867378812268025687451817912749049804226253568",
  "regulator": "187621324321847.995746680900951633822892038682861337427887352384335262033",
  "points": [
    [
      "19341774452",
      "2689933110740516"
    ],
    [
      "5319710150",
      "-387965438739538"
    ],
    [
      "26280717566/25",
      "4251553525442914/125"
    ],
    [
      "246356325585/1024",
      "-119408048627167641/32768"
    ],
    [
      "10185256278/289",
      "-3341177299619742/4913"
    ],
    [
      "10878762253/1764",
      "55920051100026917/74088"
    ],
    [
      "-21566752802/729",
      "16804572755546818/19683"
    ],
    [
      "-867465551365/11881",
      "-995340774145367248/1295029"
    ],
    [
      "-120443436422/1521",
      "-42586175434961510/59319"
    ],
    [
      "-103534214",
      "168402594986"
    ],
    [
      "-103292776",
      "186691796588"
    ],
    [
      "-93614184",
      "516091484436"
    ],
    [
      "-82336258",
      "685640223686"
    ],
    [
      "43669699",
      "676988195312"
    ],
    [
      "58010630",
      "704205329938"
    ],
    [
      "87759811",
      "906843619264"
    ],
    [
      "222772626",
      "3240709229886"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 17 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_17.tsv.gz:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-31 23:09:08",
  "updated_at": "2026-10-31 23:09:08"
}