{
  "id": 5498,
  "curve_key": "0:-59883646944600",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "69309776556"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    3
  ],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 63.44684915568765,
  "faltings_height": 3.3448933387655995,
  "conductor": "7485455868075",
  "bad_primes": [
    "3",
    "5",
    "31",
    "43",
    "79"
  ],
  "discriminant": "-2075261094551794511266875",
  "regulator": "138173402.858430041133341496886647993445732904087",
  "points": [
    [
      "2673476711435825641/677345284636164",
      "6375536685973841378214014783/17628492194910385928712"
    ],
    [
      "1471102376030870360804281/4190897221468937604",
      "1784286921997433042323692406161552775/8579471093788049760861357192"
    ],
    [
      "-7474516509169964951/7839360641146896",
      "181586958065230459936695113771/694098276822291319930944"
    ],
    [
      "1672195204486820240209/451520465978831076",
      "105147097353873879233867616560885/303400407959265799811713176"
    ],
    [
      "-147849574968901954439/65618424107752356",
      "4043597890279532679193345336639/16808876807049960153660504"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 3-isogeny partner of hdeping’s ICARM curve #5109:\r\nhttps://elliptic-rank.icarm.cloud/curve/5109\r\n\r\nThe source model is y^2 = x^3 + x^2 - 1871363967019. Applying the standard rational 3-isogeny and the recorded rational scaling gives the target model [0,0,1,0,69309776556]. The five submitted points are exact transported points.\r\n\r\nPARI/GP 2.17.4 returned rank bounds [5,5], torsion Z/3Z, conductor 7485455868075, and minimal discriminant -2075261094551794511266875. Exact quadratic-character certification at 12 good primes gives an F2 matrix of rank 5, proving the five submitted points independent modulo torsion.",
  "created_at": "2026-10-22 12:45:17",
  "updated_at": "2026-10-22 12:45:17"
}