{
  "id": 6321,
  "curve_key": "131033042635896121:-47441622683975925608114669",
  "ainvs": [
    "1",
    "1",
    "0",
    "-2729855054914502",
    "54909284376421418795016"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 118.24308438187157,
  "faltings_height": 7.571938549396313,
  "conductor": "141203664385549654650538839647975847667590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "4706788812851655155017961321599194922253"
  ],
  "discriminant": "-529513741445811204939520648679909428753462500",
  "regulator": "40999870532799.17497547635919190788848096872979887743106457747167883030",
  "points": [
    [
      "-72271363/16",
      "16584392286401/64"
    ],
    [
      "688217657",
      "-18004399905316"
    ],
    [
      "-5981033401/100",
      "65028026850887/1000"
    ],
    [
      "16524268883/484",
      "-413176289696653/10648"
    ],
    [
      "768041476/25",
      "-785898657716/125"
    ],
    [
      "43676353443/1444",
      "-189020301907197/54872"
    ],
    [
      "51698399662/1681",
      "449714946392584/68921"
    ],
    [
      "237414955097/4096",
      "79251351993506621/262144"
    ],
    [
      "355046345607/5476",
      "157178212188665991/405224"
    ],
    [
      "-238238497/4",
      "631157116147/8"
    ],
    [
      "18064567",
      "107185276139"
    ],
    [
      "24974132",
      "48050724884"
    ],
    [
      "117959903/4",
      "57648008947/8"
    ],
    [
      "30049057",
      "3504346059"
    ],
    [
      "30082007",
      "3418812734"
    ],
    [
      "32728442",
      "24933255044"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 16 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_16.tsv.gz:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-11-01 00:11:30",
  "updated_at": "2026-11-01 00:11:30"
}