{
  "id": 6371,
  "curve_key": "4212863325284683321:-12181710449363161636630963565",
  "ainvs": [
    "1",
    "1",
    "0",
    "-87767985943430902",
    "14099201872415146640041480"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 129.33946638848735,
  "faltings_height": 8.801674050556171,
  "conductor": "165139730720856957117506153800889492719508461714386",
  "bad_primes": [
    "2",
    "3",
    "43",
    "7433",
    "18523",
    "828520499779057",
    "5611166402062169654413859"
  ],
  "discriminant": "-42606050525981094936316587680629489121633183122311588",
  "regulator": "3969749013831059.4277821765924998864793925275480365987641754559162341551267",
  "points": [
    [
      "416319946",
      "7050832077490"
    ],
    [
      "-86398601",
      "4586685965614"
    ],
    [
      "-88134941",
      "-4598870629061"
    ],
    [
      "-166596138",
      "-4908812166064"
    ],
    [
      "251583549",
      "-2818284887413"
    ],
    [
      "-282498166",
      "-4043207672398"
    ],
    [
      "135431572",
      "2167117624756"
    ],
    [
      "199913908",
      "2131292606980"
    ],
    [
      "99527062",
      "2519829392602"
    ],
    [
      "-84185276",
      "4570746570364"
    ],
    [
      "1716069535/4",
      "59547737800355/8"
    ],
    [
      "207270907",
      "2193538256842"
    ],
    [
      "73432615",
      "2837240753755"
    ],
    [
      "-213571388",
      "4806597895936"
    ],
    [
      "-225673004",
      "-4734116082860"
    ],
    [
      "-274642994",
      "4182012503320"
    ],
    [
      "22162238",
      "-3487840232728"
    ],
    [
      "6772164",
      "-3674936482628"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Layr-Labs/elliptic-rank-challenge-public,\r\nsubmission/board/1-18-m10-a.ec, commit\r\ndebf8f35561f00231e8c084c95b7d4e68337de78.\r\n\r\nThe public file contains 18 rational points on the displayed generalized\r\nWeierstrass model. All 18 points were rechecked exactly. The minimal\r\ndiscriminant is\r\n-42606050525981094936316587680629489121633183122311588.\r\nThe conductor is 165139730720856957117506153800889492719508461714386.\r\nNaive height is 129.33946638848735. Source attribution remains with Layr-Labs.",
  "created_at": "2026-11-01 19:40:19",
  "updated_at": "2026-11-01 19:40:19"
}