{
  "id": 12,
  "curve_key": "1296296795598284266484863302974277781668866621848145181827394481:-47742962588359813275036508446728062178987599342510036076588219145857596371879546057522868465129",
  "ainvs": [
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    "0",
    "0",
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    "55258058551342376475736699591118191821521067032535079608372404779149413277716173425636721497"
  ],
  "rank_lower_bound": 29,
  "naive_height": 436.0124906483259,
  "faltings_height": 34.235440688657754,
  "conductor": "188691278153039213628440510802703336227022485808859170041743892297765880547867276243424847942033952274950770795963060482541371967126966027206485174370",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "31",
    "41",
    "43",
    "61",
    "233",
    "241",
    "4139",
    "678146849364709860535420504397393",
    "159788990966780131363155786084695062643236502969",
    "4402149008473369392540402625019227412319473055901"
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  "discriminant": "-58514056884179895803252795545068205623215359270190478217393508483140281138663769634024489915971980794469429246265449489823479442097938729025702174957426421151737866434992604323840000000",
  "regulator": "1433744182671713097629179252379019849.49384267391518181639888988960560090198905327978618140977503",
  "points": [
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    ],
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    ],
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      "5184894285212178249566461261834",
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      "-4469171023687146502067179612166",
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    ],
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      "-5328058719935886182106003119366",
      "6920588147379497633202935557367499676224350083"
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      "5380268474895377355583039694554",
      "8105660240030025092450118297303424395856037443"
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      "17069233487425098088940203248484",
      "67583677272795299213867443505411893525786510633"
    ],
    [
      "5215432542403430758248050783794",
      "7501515746204716855921710958364078294243814643"
    ],
    [
      "2838942178046024039763692432122",
      "1212346280964590308944175800544505700108208003"
    ],
    [
      "243146882395382015946366404808154/81",
      "811625272160726332199288136187427505366582108107/729"
    ],
    [
      "2558229016839511149831260080762",
      "1706598395830079994387505244133382709649637123"
    ],
    [
      "2361253942905600810977556672634",
      "2157503396243552448798851089310708763298766083"
    ],
    [
      "2678312077644931683114439906234",
      "1462722361020796436741527433473386115047618883"
    ],
    [
      "3379397084927230910084852603902",
      "1608494167359575995485655188349208450365853755"
    ],
    [
      "3632407730870998917912491355514",
      "2255654937037700801978158381185619053396712963"
    ],
    [
      "2428778263277521959543043930234",
      "1998325023610603606161737305486867803334410883"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Found by Elkies - Klagsbrun (2024). A historical rank ≥ 29 record, via Dujella's elliptic-curve rank-records tables.",
  "created_at": "2026-05-27 22:11:56",
  "updated_at": "2026-07-02 01:49:24"
}