{
  "id": 3603,
  "curve_key": "21293480976334360437196641:-85115809144204983796939240742906476689",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-443614187006965842441597",
    "98513667991088894052468455283418821"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "naive_height": 174.96132960083474,
  "faltings_height": 12.568569283288028,
  "conductor": "47491363856755122892643998195872310287759933770",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "13",
    "17",
    "59",
    "223",
    "2358411632341",
    "817640650132716299516483"
  ],
  "discriminant": "1394690915226111318270004923984400411925026433257830677990481927040000000",
  "regulator": "639763390656740254.0140958548954135227327520103373697318349667275338471",
  "points": [
    [
      "529821353311",
      "110471017586829144"
    ],
    [
      "617561381011",
      "245114989132044744"
    ],
    [
      "-410266707433800689/720801",
      "249792506699507065232080456/611960049"
    ],
    [
      "-6861127506103041/12769",
      "615125443693292122727368/1442897"
    ],
    [
      "-7992568932729/49",
      "139973190789346268768/343"
    ],
    [
      "136227274631319/529",
      "447431996486286655248/12167"
    ],
    [
      "541945286833549/2209",
      "6922795366023896631812/103823"
    ],
    [
      "2164851811514239/3249",
      "58196819593453278939592/185193"
    ],
    [
      "11858489024285131/64516",
      "2495152451345948153240711/16387064"
    ],
    [
      "3143726541054599/2209",
      "159141970013211920645912/103823"
    ],
    [
      "13912088661220439/11449",
      "1425307518991391758547992/1225043"
    ],
    [
      "46373964525388361/201601",
      "8414494998034104787294906/90518849"
    ],
    [
      "67928602103303551/1681",
      "17701917264632322609810504/68921"
    ],
    [
      "104706686953542711/10201",
      "33811557527305455773699944/1030301"
    ],
    [
      "493728647459937751/1879641",
      "27291877818327809227634584/2576987811"
    ],
    [
      "1010632146748927039/552049",
      "955079944848716360898242808/410172407"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = 85/531 of the rank-11 fibration of X163, y^2 - (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #718 (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 19:08:54",
  "updated_at": "2026-09-29 19:08:54"
}