{
  "id": 3654,
  "curve_key": "3574973495856050458225782273788105425:-6750698611783564628485254332166486056302427060954985625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-74478614497001051213037130703918863",
    "7813308578453199795281011676368530519633974132260217"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 252.50106333047273,
  "faltings_height": 18.824564090152684,
  "conductor": "4037723001611237548976485813408801349432131894744731730350",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "41",
    "71",
    "79",
    "97",
    "151",
    "163",
    "179",
    "191",
    "193",
    "199",
    "239",
    "811",
    "1481",
    "2179",
    "21563",
    "392599",
    "438143597"
  ],
  "discriminant": "68163435661531471885519549668862676346305753044573207755789547466526004476749194512786826762265664000000",
  "regulator": "6102959932109307084.566269323407833189864264185422777930493446259300240",
  "points": [
    [
      "-310720537090836082",
      "30921345983613377367432077"
    ],
    [
      "-237906260208257158",
      "109849389448240194789714629"
    ],
    [
      "-154270142490639358",
      "125026466140984196544965429"
    ],
    [
      "177288480792769598",
      "13472149756402112242668845"
    ],
    [
      "1159975142075985683/4",
      "823743855739228492917291667/8"
    ],
    [
      "586329223354907438",
      "407079511491991301643000965"
    ],
    [
      "-4268142720661780865443/913936",
      "78930722991572916201191293642622029/873722816"
    ],
    [
      "-363974277303453525292/5329",
      "43635200499636613673578116110933/389017"
    ],
    [
      "-7055503944221450914/361",
      "660086647903860703699062894095/6859"
    ],
    [
      "14264963340788166713/64",
      "24479482998833027941910176273/512"
    ],
    [
      "2764409561766147910958/11449",
      "76572041912665819822750773512047/1225043"
    ],
    [
      "22230144638597768803238/214369",
      "3445401120213003698384902728765203/99252847"
    ],
    [
      "27732438078959310770542/201601",
      "1183778864131379436468527939435021/90518849"
    ],
    [
      "151529577575708468807468/923521",
      "2841093182264491090118066520788327/887503681"
    ],
    [
      "336763059968161217203582/447561",
      "184033774648337232701656011140699521/299418309"
    ],
    [
      "275188664581017270069721448/1903315129",
      "681477300669137981971591410261652163327/83035929132883"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = -115/1351 of the rank-9 fibration of X400, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #802 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:27:37",
  "updated_at": "2026-09-29 19:27:37"
}