{
  "id": 4948,
  "curve_key": "0:6048676296",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-7000783"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 45.04621058200133,
  "faltings_height": 1.8115067909584062,
  "conductor": "476053227",
  "bad_primes": [
    "3",
    "13",
    "17",
    "19"
  ],
  "discriminant": "-21172734336685347",
  "regulator": "2443.791406270974132246950063336682455837209366",
  "points": [
    [
      "841/4",
      "12111/8"
    ],
    [
      "3025/4",
      "-165027/8"
    ],
    [
      "1993/4",
      "86415/8"
    ],
    [
      "10417/36",
      "896419/216"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4919, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4919.\r\n\r\nThe source model is y^2 + y = x^3 + 259288. 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 = 1037153/4. Applied the degree-3 isogeny X = (x^3 + 4B)/x^2, V = Y*(x^3 - 8B)/x^3, then set y' = V - 1/2. The resulting minimal model is y'^2 + y' = X^3 - 7000783.\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 476053227. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:35:27",
  "updated_at": "2026-10-20 23:35:27"
}