{
  "id": 4937,
  "curve_key": "0:17011944",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-19690"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 33.298852487112434,
  "faltings_height": 0.8325602830509979,
  "conductor": "229740003",
  "bad_primes": [
    "3",
    "2917"
  ],
  "discriminant": "-167480462187",
  "regulator": "6263.456972140580485722736507855081408989093685",
  "points": [
    [
      "2188/81",
      "2917/729"
    ],
    [
      "2890/9",
      "155303/27"
    ],
    [
      "2944/9",
      "-159706/27"
    ],
    [
      "2515510/47961",
      "-3712729985/10503459"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4794, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4794.\r\n\r\nThe source model is y^2 + y = x^3 + 729. 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 = 2917/4. 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 - 19690.\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 229740003. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:13:00",
  "updated_at": "2026-10-20 23:13:00"
}