{
  "id": 4947,
  "curve_key": "0:9199656",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-10648"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 32.0693533000317,
  "faltings_height": 0.7301020174609368,
  "conductor": "48977818587",
  "bad_primes": [
    "3",
    "14197"
  ],
  "discriminant": "-48977818587",
  "regulator": "90884.1227427320599484436239053478957318989363518",
  "points": [
    [
      "11110/441",
      "672211/9261"
    ],
    [
      "799105/19044",
      "659550581/2628072"
    ],
    [
      "13954/81",
      "1646263/729"
    ],
    [
      "14188/9",
      "1689965/27"
    ],
    [
      "1150300/441",
      "-1233724472/9261"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4930, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4930.\r\n\r\nThe source model is y^2 + y = x^3 + 287489. Its public entry supplies five 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 = 1149957/4. 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 - 10648.\r\n\r\nFive 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 48977818587. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:34:12",
  "updated_at": "2026-10-20 23:34:12"
}