{
  "id": 6251,
  "curve_key": "13574170295040576:-1619940925780638563145600",
  "ainvs": [
    "0",
    "0",
    "0",
    "-282795214480012",
    "1874931627060924262900"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 111.488863829738,
  "faltings_height": 7.194389719712712,
  "conductor": "130908082123329853454719245346731068283032",
  "bad_primes": [
    "2",
    "17",
    "1291",
    "6997",
    "11213",
    "14967607",
    "634914494977021178191"
  ],
  "discriminant": "-71213996675091440279367269468621701145969408",
  "regulator": "55815958947143.54044064231078859335501205588946324460494263071271732079",
  "points": [
    [
      "-110496006/49",
      "-17154024965734/343"
    ],
    [
      "8646560918",
      "-804015252596254"
    ],
    [
      "92609913/49",
      "-12589550534329/343"
    ],
    [
      "17715291458/2401",
      "-1621908295043254/117649"
    ],
    [
      "2610080364/289",
      "37271191205446/4913"
    ],
    [
      "1358575401/25",
      "47924222794351/125"
    ],
    [
      "239153789186/3721",
      "113306978025505262/226981"
    ],
    [
      "645385341668/4489",
      "515081674945547786/300763"
    ],
    [
      "227642683449/676",
      "108479840721149581/17576"
    ],
    [
      "-18860743",
      "22346636153"
    ],
    [
      "-17884350",
      "34817112490"
    ],
    [
      "-6364774",
      "58455282442"
    ],
    [
      "8207014",
      "10334960926"
    ],
    [
      "9463466",
      "6799274998"
    ],
    [
      "9738334",
      "6671861186"
    ],
    [
      "12399172",
      "16575500222"
    ]
  ],
  "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": "2026-10-31 22:52:32",
  "updated_at": "2026-10-31 22:52:32"
}