{
  "id": 4932,
  "curve_key": "0:249708744",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-289015"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 38.67161154531702,
  "faltings_height": 1.280290204568047,
  "conductor": "16499659401",
  "bad_primes": [
    "3",
    "47",
    "911"
  ],
  "discriminant": "-36084755109987",
  "regulator": "64459.8544219158129033428616938316449445325791549",
  "points": [
    [
      "32169/484",
      "716791/10648"
    ],
    [
      "42825/4",
      "-8862295/8"
    ],
    [
      "44545/144",
      "-9356383/1728"
    ],
    [
      "75585/1024",
      "-11038945/32768"
    ],
    [
      "1858665/14884",
      "2337476297/1815848"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4712, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4712.\r\n\r\nThe source model is y^2 + y = x^3 + 10704. 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 = 42817/4. 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 - 289015.\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 16499659401. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:06:23",
  "updated_at": "2026-10-20 23:06:23"
}