{
  "id": 4934,
  "curve_key": "0:11086632",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-12832"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 32.44250123235385,
  "faltings_height": 0.7611976784877825,
  "conductor": "97572627",
  "bad_primes": [
    "3",
    "1901"
  ],
  "discriminant": "-71130445083",
  "regulator": "5187.126144449091927249760014176533222305366869",
  "points": [
    [
      "91873/3844",
      "6708811/238328"
    ],
    [
      "1558/49",
      "47496/343"
    ],
    [
      "2026/25",
      "-90149/125"
    ],
    [
      "1385704/225",
      "1631192608/3375"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4709, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4709.\r\n\r\nThe source model is y^2 + y = x^3 + 475. 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 = 1901/4. 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 - 12832.\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 97572627. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:09:02",
  "updated_at": "2026-10-20 23:09:02"
}