{
  "id": 4949,
  "curve_key": "0:8546472",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-9892"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 31.92205824835632,
  "faltings_height": 0.717827429821322,
  "conductor": "349337043",
  "bad_primes": [
    "3",
    "11",
    "109"
  ],
  "discriminant": "-42269782203",
  "regulator": "6319.819386344295641477266476139359829283989336",
  "points": [
    [
      "10102/441",
      "422612/9261"
    ],
    [
      "13198/9",
      "-1516231/27"
    ],
    [
      "13432/81",
      "-1555397/729"
    ],
    [
      "14314/225",
      "-1681012/3375"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4922, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4922.\r\n\r\nThe source model is y^2 + y = x^3 + 267077. Its public entry supplies four rational points and no commentary identifying an earlier source.\r\n\r\nCompleted the square with Y = y + 1/2, giving Y^2 = x^3 + B with B = 1068309/4. Applied the degree-3 isogeny U = (x^3 + 4B)/x^2, V = Y*(x^3 - 8B)/x^3, then set X = U/9 and y' = V/27 - 1/2. The resulting minimal model is y'^2 + y' = X^3 - 9892.\r\n\r\nFour supplied rational points transported through this map and checked exactly on the target curve. Rational torsion trivial. Same rank and conductor as the source; conductor 349337043. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:36:36",
  "updated_at": "2026-10-20 23:36:36"
}