{
  "id": 3611,
  "curve_key": "8274064766522205975735111376:-754667041652273006013417120556914943762624",
  "ainvs": [
    "0",
    "1",
    "0",
    "-172376349302545957827814820",
    "873457224134517779658354151991968209600"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "naive_height": 192.85419054862336,
  "faltings_height": 13.882285501880501,
  "conductor": "11338339931713010411611348392408157126038267924244707240",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "37",
    "47",
    "1741603",
    "2235167387686907731",
    "63093275975701275781"
  ],
  "discriminant": "-1781624571339422345390780819676060745406460628585776253945779892186304220000000",
  "regulator": "748024566770250124070.54905190318539547517324036539829274548957065398973306",
  "points": [
    [
      "8985215258335",
      "7073317937201238450"
    ],
    [
      "862709029285510",
      "25336493662115431545750"
    ],
    [
      "-259050565264982942/17161",
      "13449003475144564004511834/2248091"
    ],
    [
      "-115787254097640215/30976",
      "208708762100710371709502475/5451776"
    ],
    [
      "-101826874049507585/16129",
      "84707156827169875967834250/2048383"
    ],
    [
      "-26277085256723510/1849",
      "1692077074025939564213250/79507"
    ],
    [
      "122690600837590/9",
      "877806540992762116750/27"
    ],
    [
      "286710121143490/49",
      "2769004436786593656750/343"
    ],
    [
      "33346168465146835/3721",
      "1579091328333386815720500/226981"
    ],
    [
      "87610291621368595/22201",
      "52789918327365046234155840/3307949"
    ],
    [
      "100544088653745190/12769",
      "3010756599480993844425750/1442897"
    ],
    [
      "207830835291651550/10609",
      "77380736222450965570193070/1092727"
    ],
    [
      "245875510205750590/2209",
      "121107165875964590609537250/103823"
    ],
    [
      "362291090397319435/58081",
      "89549193950693773022727000/13997521"
    ],
    [
      "6082226991263443570/769129",
      "1484343333549000514297440810/674526133"
    ],
    [
      "9227201297095422190/1495729",
      "12248852766073563539782332450/1829276567"
    ],
    [
      "18018434717759791540/877969",
      "63615266134756423388753797800/822656953"
    ],
    [
      "51280718647330055290/7038409",
      "38758562092114711445930695650/18672899077"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = 9 of the rank-17 fibration of X1092, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #1842 (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 19:18:59",
  "updated_at": "2026-09-29 19:18:59"
}