{
  "id": 4931,
  "curve_key": "0:3624173928",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-4194646"
  ],
  "rank_lower_bound": 6,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 44.021784434705964,
  "faltings_height": 1.726137945350459,
  "conductor": "10426698055107",
  "bad_primes": [
    "3",
    "359",
    "577"
  ],
  "discriminant": "-7601062882173003",
  "regulator": "3840694.2242134368194097928158643930907098625402152",
  "points": [
    [
      "29833081/184900",
      "5955492729/79507000"
    ],
    [
      "472552/2809",
      "111960229/148877"
    ],
    [
      "637054/625",
      "-507468658/15625"
    ],
    [
      "739078/2401",
      "-587980527/117649"
    ],
    [
      "2669812/16129",
      "1194777671/2048383"
    ],
    [
      "9236554/42025",
      "21828661158/8615125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4819, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4819.\r\n\r\nThe source model is y^2 + y = x^3 + 155357. Its public entry supplies six 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 = 621429/4. 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 - 4194646.\r\n\r\nSix 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 10426698055107. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:04:44",
  "updated_at": "2026-10-20 23:04:44"
}