{
  "id": 4946,
  "curve_key": "0:5636027304",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-6523180"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 44.904890551083454,
  "faltings_height": 1.79973012171525,
  "conductor": "23283402921",
  "bad_primes": [
    "3",
    "19",
    "2677"
  ],
  "discriminant": "-18382409589949947",
  "regulator": "39440.8691495126522029497975580417693712550090773",
  "points": [
    [
      "2164/9",
      "73324/27"
    ],
    [
      "2658",
      "137011"
    ],
    [
      "966370/9",
      "949981508/27"
    ],
    [
      "196617/484",
      "-82838111/10648"
    ],
    [
      "16528/81",
      "1023524/729"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4914, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4914.\r\n\r\nThe source model is y^2 + y = x^3 + 241599. 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 = 966397/4. 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 model is y'^2 + y' = X^3 - 6523180.\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 23283402921. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:32:23",
  "updated_at": "2026-10-20 23:32:23"
}