{
  "id": 3589,
  "curve_key": "2064654677140517342569406656:-93986467907352931291347634099581455818240",
  "ainvs": [
    "0",
    "1",
    "0",
    "-43013639107094111303529305",
    "108780634152014517781579619207784767799"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "naive_height": 188.68793888048472,
  "faltings_height": 13.519892149875643,
  "conductor": "17346348574378923720434937981014495076047771460206208",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "23",
    "31",
    "30325439",
    "354167135908081",
    "346648208624175386833"
  ],
  "discriminant": "-18662262217531282821665525866223065740254630099610002247525389188656473776128",
  "regulator": "476951495200295.04552246507726719265450428388009060658645382307704864999048",
  "points": [
    [
      "3543727205947",
      "924211106332426836"
    ],
    [
      "3544030174459",
      "923336019387273492"
    ],
    [
      "3680232644863",
      "570893722736637300"
    ],
    [
      "3797695607935",
      "447392549964391668"
    ],
    [
      "3812247507346",
      "454169082913050561"
    ],
    [
      "3819094980475",
      "459150423176577132"
    ],
    [
      "3822244803151",
      "461814428854142364"
    ],
    [
      "3850690555759",
      "495739921607602308"
    ],
    [
      "3877462711897",
      "541670823694064064"
    ],
    [
      "3958361763205",
      "734293654622339868"
    ],
    [
      "517670996617",
      "9308729660323397304"
    ],
    [
      "635837552971",
      "9038141927221997436"
    ],
    [
      "2302115818777",
      "4686028604589508176"
    ],
    [
      "4265107453381",
      "1705876600341477564"
    ],
    [
      "4454625714313",
      "2359488121283933640"
    ],
    [
      "5256539373145",
      "5284152706299584832"
    ],
    [
      "5766717429819",
      "7246067377232151468"
    ],
    [
      "13583890493563",
      "45066792785156312940"
    ]
  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "Specialization at T = 8 of the rank-17 fibration of X1008 given by:\r\ny^2 - (Lx+B)y = x(x+D)(x+E),\r\nwhere\r\nB = pq(L+p+q) - pE - qD,\r\nL = 94992T^2 + 43200T - 74684,\r\np = 45650T^2 - 3480T + 2996,\r\nq = 7132T^2 - 71704T - 112100,\r\nD = 5(101326060T^4 + 455923735T^3 - 335745592T^2 - 107751313T - 99088206),\r\nE = 2(537101785T^4 - 5857182939T^3 - 5207884583T^2 + 312473955T - 77661626).",
  "created_at": "2026-09-28 22:51:51",
  "updated_at": "2026-09-28 22:51:51"
}