{
  "id": 4933,
  "curve_key": "0:364505832",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-421882"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 39.42810621856998,
  "faltings_height": 1.3433314273391268,
  "conductor": "35157375009",
  "bad_primes": [
    "3",
    "62501"
  ],
  "discriminant": "-76889179144683",
  "regulator": "77382.5647598700192790808981997579849825682876538",
  "points": [
    [
      "46876/625",
      "62501/15625"
    ],
    [
      "57588/289",
      "13443746/4913"
    ],
    [
      "62376/25",
      "15578249/125"
    ],
    [
      "64698/169",
      "-16395566/2197"
    ],
    [
      "3111126/21025",
      "5116277749/3048625"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4779, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4779.\r\n\r\nThe source model is y^2 + y = x^3 + 15625. 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 = 62501/4. 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 - 421882.\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 35157375009. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:07:29",
  "updated_at": "2026-10-20 23:07:29"
}