{
  "id": 5615,
  "curve_key": "0:9095805367383255573024",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-10527552508545434691"
  ],
  "rank_lower_bound": 12,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 101.12420062297817,
  "faltings_height": 6.484672627706475,
  "conductor": "111694998055108364588230797740636196",
  "bad_primes": [
    "2",
    "3",
    "7",
    "23",
    "6555427",
    "52776277"
  ],
  "discriminant": "-47878284306318310697474307913119186687792",
  "regulator": "864279650522857072.73016545519923832659263193024526740606642878",
  "points": [
    [
      "355013472400781707/67271240689",
      "203811333294734913222106192/17447939883783863"
    ],
    [
      "7957335971569993/295936",
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    ],
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      "483792494300255107/130128297289",
      "-300060926146434745460936692/46941571065952837"
    ],
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      "310647199107412740722439817/288951507122241604",
      "5475214796315512370897669309595691866683/155323599358751694277045192"
    ],
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      "8048360095768244022961339/2238190924713922369",
      "20082435237642800239091815505631641560/3348464474728059414067458847"
    ],
    [
      "177847375478120564161/73041534116356",
      "-1234044545443894477594939269185/624244650584184874504"
    ],
    [
      "7990035938989026441286191/620932849850055625",
      "-22529290475926979774951293589649197886/489290692581931143356453125"
    ],
    [
      "11660051634242103734691838713/948332234652371587216",
      "-1255501791773678914595337840722633866709619/29203894394242709784989602883264"
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    [
      "3181253683356842668243017782360523/365758279698471687768370081",
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    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Exact-rank-12 Mordell curve obtained by the rational 3-isogeny from y^2=x^3+389909352168349433, discovered using the Burkhardt quartic construction with parameters (u,v,w)=(1,3,-3) and specialization t=491/711.",
  "created_at": "2026-10-23 23:08:40",
  "updated_at": "2026-10-23 23:08:40"
}