{
  "id": 4945,
  "curve_key": "0:7474248",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-8651"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 31.65394814034723,
  "faltings_height": 0.6954849208205643,
  "conductor": "32328925443",
  "bad_primes": [
    "3",
    "34603"
  ],
  "discriminant": "-32328925443",
  "regulator": "77358.2415278383859027342031351424519239968115924",
  "points": [
    [
      "11201/100",
      "1181301/1000"
    ],
    [
      "11513/16",
      "1235283/64"
    ],
    [
      "998281/14400",
      "-985252571/1728000"
    ],
    [
      "14201/400",
      "-1523949/8000"
    ],
    [
      "17393/676",
      "-1617923/17576"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4910, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4910.\r\n\r\nThe source model is y^2 + y = x^3 + 233570. 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 = 934281/4. Applied the standard degree-3 isogeny U = (x^3+4*B)/x^2, V = Y*(x^3-8*B)/x^3, followed by X = U/9 and y' = V/27 - 1/2. The resulting integral model is y'^2 + y' = X^3 - 8651.\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 32328925443. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:29:27",
  "updated_at": "2026-10-20 23:29:27"
}