{
  "id": 6248,
  "curve_key": "9947620317449136:-991994216914985008809240",
  "ainvs": [
    "0",
    "0",
    "1",
    "-207242089946857",
    "1148141454762714130566"
  ],
  "rank_lower_bound": 15,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 110.5083292602043,
  "faltings_height": 6.91967591988291,
  "conductor": "15459554382087158087678575436367936383",
  "bad_primes": [
    "53",
    "223",
    "313",
    "4178995477333474823442779343589"
  ],
  "discriminant": "182716473241888121438273083082432640110677",
  "regulator": "379703638788.09742037480125380163185886167201836173705523495939384587",
  "points": [
    [
      "18570632",
      "60860073189"
    ],
    [
      "264270378",
      "-4289838564517"
    ],
    [
      "49149833/4",
      "170991163287/8"
    ],
    [
      "21473330",
      "-81236690628"
    ],
    [
      "5788422097/576",
      "-123931800606439/13824"
    ],
    [
      "306191833/36",
      "188314243831/216"
    ],
    [
      "66603478978/7921",
      "159655606556427/704969"
    ],
    [
      "34367609/4",
      "-10729065873/8"
    ],
    [
      "23872597202/2809",
      "-124161029317284/148877"
    ],
    [
      "-7234352",
      "47631793266"
    ],
    [
      "7158514",
      "5606179971"
    ],
    [
      "7939866",
      "1791053300"
    ],
    [
      "32651401/4",
      "4822352919/8"
    ],
    [
      "8817493",
      "2515916333"
    ],
    [
      "417037434/49",
      "309849249900/343"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 15 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_15.tsv.gz:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-31 22:41:52",
  "updated_at": "2026-10-31 22:41:52"
}