{
  "id": 6327,
  "curve_key": "376526706814889221082736:-231089064985139741073454471939111320",
  "ainvs": [
    "0",
    "0",
    "1",
    "-7844306391976858772557",
    "267464195584652478094276009188786"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 162.85622253544267,
  "faltings_height": 11.2887299861252,
  "conductor": "938202090638277428589512723668761222446243676054957512376898871",
  "bad_primes": [
    "13",
    "2881205209",
    "5253768880146954443",
    "4767688679201435638271846533007041"
  ],
  "discriminant": "-12196627178297606571663665407693895891801167788714447660899685323",
  "regulator": "3571859899288373057.466428849936643053604066243331270647901105632583862058394",
  "points": [
    [
      "51614930829",
      "297080726924741"
    ],
    [
      "51682053209",
      "314465899866098"
    ],
    [
      "50455937682",
      "350956383302544"
    ],
    [
      "50380713559",
      "373618090741226"
    ],
    [
      "49590586104",
      "644138294197833"
    ],
    [
      "53220033146",
      "853743105090024"
    ],
    [
      "48794759943",
      "938076566443893"
    ],
    [
      "23661828457",
      "9751994575132205"
    ],
    [
      "86994496427",
      "-15602267446392595"
    ],
    [
      "53894906061",
      "1114659492170309"
    ],
    [
      "3783520358",
      "15422038252113356"
    ],
    [
      "-14157199335",
      "-19382469652718478"
    ],
    [
      "-14817918186",
      "-19505048199571812"
    ],
    [
      "166098954881/4",
      "29211167408374363/8"
    ],
    [
      "38371535165",
      "4792013670259802"
    ],
    [
      "-63620669235",
      "-22561335548196283"
    ],
    [
      "-95535825833",
      "-12037940870557206"
    ],
    [
      "-45512727859",
      "-23026170566991430"
    ],
    [
      "5095172539933/81",
      "-3490765121601632726/729"
    ]
  ],
  "submitter": "The Wren",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-11-01 01:09:59"
    }
  ],
  "commentary": "Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 19 (19 independent rational points) in Layr-Labs elliptic-rank-challenge-public, file submission/board/1-19-mestre-own.ec, commit 50996b75f386f17ed01450a3f90ece81d435f51a:\r\nhttps://github.com/Layr-Labs/elliptic-rank-challenge-public",
  "created_at": "2026-11-01 01:08:04",
  "updated_at": "2026-11-01 01:09:59"
}