{
  "id": 4757,
  "curve_key": "0:28647857212331176596650472",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-33157242143901824764642"
  ],
  "rank_lower_bound": 14,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 117.23424176066017,
  "faltings_height": 7.8271760558466426,
  "conductor": "651497900201089941708666232118910606092447907",
  "bad_primes": [
    "3",
    "293",
    "7459",
    "170389",
    "4397072149"
  ],
  "discriminant": "-474941969246594567505617683214685831841394524203",
  "regulator": "466836721365196397143.675184261737252540077379450724508198027766919",
  "points": [
    [
      "3684219550495548478522/114671950833001",
      "3155910407433421859339478925078/1227964470823240375499"
    ],
    [
      "4227163697499665779798/77708579671009",
      "244899346376000172212105404901091/685020323819123074223"
    ],
    [
      "280486158834371611834969/4189272550668100",
      "140102693295948356330094754314930953/271148948240246998579000"
    ],
    [
      "4603713719706608396272/45653657049001",
      "307273323778754641469239287195753/308470301612180457749"
    ],
    [
      "4639997157962970900778/41999563219849",
      "312154902765447683743866119907631/272186863355817953243"
    ],
    [
      "4909761412274719447828/1803802105249",
      "344025175746277870493358613610101/2422609044069406193"
    ],
    [
      "4912171847175891512896/52920702025",
      "344278837299459083064594290788569/12174142897341125"
    ],
    [
      "4912295862846616019422/232132203601",
      "-344291874595171968366272206700763/111841527827165401"
    ],
    [
      "5068652940300290899822/29037020737201",
      "-359733539668199658773767092368158/156468918981502045801"
    ],
    [
      "5414786305003136268772/63214441464001",
      "-387795347387745208960456575185253/502602283684347414751"
    ],
    [
      "26446263442651037158738/774017667095929",
      "1766658457155680044197162310013754/21534079421332248304717"
    ],
    [
      "370665442800050788613788/5114369908721329",
      "215618098289833713375089172424041654/365753258778731999759767"
    ],
    [
      "35645694694032170001956497/430691722569113476",
      "206501811769628268719238019451965571293/282650519333342140122393224"
    ],
    [
      "2436974646091584272932682896/1810923440757858025",
      "120302197879045539715675370836789830415806/2436969733907562954143828875"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Mordell curve y^2 = x^3 + -2122063497209716784937072. Source: N. D. Elkies, 'j=0, rank 15; also 3-rank 6 and 7 in real and imaginary quadratic fields', NMBRTHRY post, 30 Dec 2009, https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;6a3fad67.0912&S=. Points are images of Elkies' points on y^2 = x^3 + 78594944341100621664336 under the 3-isogeny (x,y) -> ((x^3+4k)/x^2, y(x^3-8k)/x^3).",
  "created_at": "2026-10-20 21:28:41",
  "updated_at": "2026-10-20 21:28:41"
}