{
  "id": 4950,
  "curve_key": "0:-1046614169068128",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "1211358991977"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 69.16867349592711,
  "faltings_height": 3.821712033785555,
  "conductor": "72463733700915237055236",
  "bad_primes": [
    "2",
    "3",
    "1433",
    "31308547"
  ],
  "discriminant": "-633912742415606493759204528",
  "regulator": "413464902953.44635224041432963180039611049556457293750867",
  "points": [
    [
      "-130793487953/13329801",
      "25131893730729940/48667103451"
    ],
    [
      "-129012664029/13653025",
      "30587241174653394/50447927375"
    ],
    [
      "-80657239037/21372129",
      "106304692396253050/98803352367"
    ],
    [
      "-29315960529/28249225",
      "165175566434095644/150144630875"
    ],
    [
      "999126932143/111576969",
      "1637083920213375220/1178587523547"
    ],
    [
      "186528436407471/3266694025",
      "2555794417269062173644/186707896998875"
    ],
    [
      "11268724218897/3211942276",
      "203889255817267498905/182033616550024"
    ],
    [
      "38289638186769/5412544900",
      "498211002021701404647/398200928293000"
    ],
    [
      "-431700957152727/72238387984",
      "19395591074057134279125/19415656015235648"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4668, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4668.\r\n\r\nThe source model is y^2 = x^3 - 44865147851. Renshaw's commentary reports finding it using a Mestre-Nagao sieve over |k| <= 10^12, with a_p computed via sextic residue classes for primes p = 1 mod 3, followed by PARI/GP ellrank certification.\r\n\r\nApplied the degree-3 isogeny X = (x^3 + 4B)/x^2, Y = y*(x^3 - 8B)/x^3 with B = -44865147851. The resulting model is Y^2 = X^3 + 1211358991977.\r\n\r\nNine 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 72463733700915237055236. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:38:23",
  "updated_at": "2026-10-20 23:38:23"
}