{
  "id": 4938,
  "curve_key": "0:59258952",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-68587"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 35.794854830348754,
  "faltings_height": 1.0405604783206912,
  "conductor": "309737763",
  "bad_primes": [
    "3",
    "1129"
  ],
  "discriminant": "-2032189463043",
  "regulator": "2794.671829438264007957219072499272166989302520",
  "points": [
    [
      "937/16",
      "23243/64"
    ],
    [
      "71881/100",
      "19269471/1000"
    ],
    [
      "1153/4",
      "-39099/8"
    ],
    [
      "1777/36",
      "-49213/216"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4796, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4796.\r\n\r\nThe source model is y^2 + y = x^3 + 2540. 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 = 10161/4. Applied the standard degree-3 isogeny X = (x^3+4*B)/x^2, V = Y*(x^3-8*B)/x^3, then set y' = V - 1/2. The resulting integral model is y'^2 + y' = X^3 - 68587.\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 309737763. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:14:10",
  "updated_at": "2026-10-20 23:14:10"
}