{
  "id": 5614,
  "curve_key": "0:-336881680273453910112",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "389909352168349433"
  ],
  "rank_lower_bound": 12,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 94.5325268909695,
  "faltings_height": 5.9353664833724205,
  "conductor": "111694998055108364588230797740636196",
  "bad_primes": [
    "2",
    "3",
    "7",
    "23",
    "6555427",
    "52776277"
  ],
  "discriminant": "-65676658856403718377879709071494083248",
  "regulator": "1626294641404.8917428842815198662472910306730761180778413152707",
  "points": [
    [
      "-518734",
      "500325727"
    ],
    [
      "7616",
      "624427573"
    ],
    [
      "721466",
      "874895377"
    ],
    [
      "741398",
      "892991785"
    ],
    [
      "918682",
      "1079469999"
    ],
    [
      "962476",
      "1132037397"
    ],
    [
      "1075084196",
      "35250372980437"
    ],
    [
      "-176006878/289",
      "1989735838735/4913"
    ],
    [
      "4273217/4",
      "10148141695/8"
    ],
    [
      "220638019/625",
      "10292406045978/15625"
    ],
    [
      "699886441/1936",
      "56321734082613/85184"
    ],
    [
      "314626688026/724201",
      "423367560444547803/616295051"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Exact-rank-12 Mordell curve discovered in October 2026 using the Burkhardt quartic construction, with parameters (u,v,w)=(1,3,-3) and specialization t=491/711.",
  "created_at": "2026-10-23 23:07:28",
  "updated_at": "2026-10-23 23:07:28"
}