{
  "id": 4969,
  "curve_key": "0:10928404008",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-12648616"
  ],
  "rank_lower_bound": 6,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 46.229262218153664,
  "faltings_height": 1.9100944273044338,
  "conductor": "94807395787347",
  "bad_primes": [
    "3",
    "223",
    "2801"
  ],
  "discriminant": "-69114591528975963",
  "regulator": "6655778.1237937823575477389847674414566586578739894",
  "points": [
    [
      "1515958/5041",
      "1364949337/357911"
    ],
    [
      "109989241/184900",
      "1118286225039/79507000"
    ],
    [
      "1861702/529",
      "2539809744/12167"
    ],
    [
      "119943241/2500",
      "-1313601590039/125000"
    ],
    [
      "1924522/1369",
      "-2663775069/50653"
    ],
    [
      "1371409876/275625",
      "-50784271783624/144703125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4968, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4968.\r\n\r\nThe source model is y^2 + y = x^3 + 468467. 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 = 1873869/4. 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 minimal model is y'^2 + y' = X^3 - 12648616.\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 94807395787347. Source-attributed existing curve.",
  "created_at": "2026-10-21 00:09:07",
  "updated_at": "2026-10-21 00:09:07"
}