{
  "id": 4176,
  "curve_key": "1729374326551863672681:-68463178362308606289964311290805",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-36028631803163826514",
    "79239789780197674490101502104"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "naive_height": 146.7061399050506,
  "faltings_height": 10.163030856591547,
  "conductor": "972088439459265420913132639723426333713908127782",
  "bad_primes": [
    "2",
    "11",
    "17",
    "23",
    "73",
    "79",
    "1781409251921861107956807775400919860443"
  ],
  "discriminant": "280610246419042224963014060069946123138051782663560804584172",
  "regulator": "110035839702498018224.139710525457658310613966769372933811140405639022206",
  "points": [
    [
      "-25760533661/4",
      "1681213937591437/8"
    ],
    [
      "4384960201",
      "74624505596909"
    ],
    [
      "-960189547044928983/369062521",
      "2794653025188616076922382390/7090060090931"
    ],
    [
      "-45768804057583279/7946761",
      "6930119208599976766754190/22401919259"
    ],
    [
      "-367753117611029/79524",
      "8596952608472635850869/22425768"
    ],
    [
      "-2728127374946/18225",
      "715752049081320220022/2460375"
    ],
    [
      "366180957168222/78961",
      "2419637922487750002440/22188041"
    ],
    [
      "1943184730049913/273529",
      "60999490549325815574566/143055667"
    ],
    [
      "2230632657713271/160801",
      "96697205856269504025424/64481201"
    ],
    [
      "4292047034624154/3667225",
      "1381098127278546717459412/7022735875"
    ],
    [
      "4465156631265598/168921",
      "291231187658335145356072/69426531"
    ],
    [
      "21434398101410302/9504889",
      "2850113796407177453827240/29303572787"
    ],
    [
      "77863997123224733/15342889",
      "9893452720016847250774190/60098096213"
    ],
    [
      "273378464511883876/112225",
      "142937108834364196487337744/37595375"
    ],
    [
      "1723405473484986036/402764761",
      "472681799195052644061543860/8083085988509"
    ],
    [
      "2357180103898667556/61701025",
      "3576650327240990533465091956/484661551375"
    ],
    [
      "168629120102921127604/14185524609",
      "1949023322590700486259844622188/1689538537505727"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Specialization at T = 3 of the K3 elliptic fibration y^2 - (Lx+B)y = x(x+D)(x+E) given in the commentary of database curve #3589; points from PARI ellrank.",
  "created_at": "2026-10-11 22:58:52",
  "updated_at": "2026-10-11 22:58:52"
}