{
  "id": 6219,
  "curve_key": "40615443852368916275313395841:-8276771722135350105594145027592095912199361",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-846155080257685755735695747",
    "9579596900619829716541065610781637526019"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 197.6440538189795,
  "faltings_height": 14.339687935271744,
  "conductor": "606467578887950117548856168527290",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "19",
    "31",
    "37",
    "137",
    "139",
    "163",
    "251",
    "145633",
    "373667527"
  ],
  "discriminant": "-871026620573830843601194479393400284371666357109003481900139590911875088384000000",
  "regulator": "214816122876.0360492063009312486872755544704777736670727377",
  "points": [
    [
      "-598404321326161780133/67092481",
      "70413826415196057033797864137006/549554511871"
    ],
    [
      "-2398334311057283997/339889",
      "24429363755750626357412669782/198155287"
    ],
    [
      "986455198917169/81",
      "23968228857243437270368/729"
    ],
    [
      "24774673063525107/841",
      "2465276929264887718067354/24389"
    ],
    [
      "34429314707008323/1849",
      "1330223599563524286602902/79507"
    ],
    [
      "45491409914040027/961",
      "8191218007846237360147246/29791"
    ],
    [
      "60081839081626243/2809",
      "5298118257836923004676522/148877"
    ],
    [
      "48538529353970619843/4826809",
      "484515350513978840218948543978/10604499373"
    ],
    [
      "61128191629525608963/7166329",
      "1047713023924741861174579568938/19184262733"
    ],
    [
      "308037527215659971163/14691889",
      "1829500907040313401386118250802/56314010537"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 8959/652 of the fibration given in curve#6190. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.",
  "created_at": "2026-10-30 23:57:36",
  "updated_at": "2026-10-30 23:57:36"
}