{
  "id": 754,
  "curve_key": "2380009385826670732075684017:-118670443967260588146094790919189405698409",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-49583528871388973584910084",
    "137350050888045484014272003399865447079"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "naive_height": 189.15433779925976,
  "faltings_height": 13.662154027116367,
  "conductor": "15251203000259881061249343205416584739119678368456217166",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "41",
    "67",
    "71",
    "1667",
    "8677484058375482423",
    "13132215161784692278819"
  ],
  "discriminant": "-347941421023127134233199319395414222408456695945653647904217611171809101152256",
  "regulator": "3172353687724361.7199080024659721020772175990326204377515112946053522096870",
  "points": [
    [
      "-8041906180091",
      "-4000987219869556291"
    ],
    [
      "-7540859247683",
      "-9079909973253166675"
    ],
    [
      "-6432364117739",
      "-13789424450354780707"
    ],
    [
      "-5645385141851",
      "-15406088037822495619"
    ],
    [
      "-4637547827459",
      "-16357167139197747667"
    ],
    [
      "-2902403497403",
      "-16025346220110127363"
    ],
    [
      "-2291056120163",
      "-15457135921373099923"
    ],
    [
      "-1014348599051",
      "-13660210601611071331"
    ],
    [
      "411889889221",
      "-10816514207464791427"
    ],
    [
      "1391258042797",
      "-8429679524069823163"
    ],
    [
      "2225787143671",
      "-6165591523305089845"
    ],
    [
      "138461435283993913/64",
      "-51521790935383263519176975/512"
    ],
    [
      "611156309929333",
      "-15107749019070459245155"
    ],
    [
      "108983282491129/25",
      "-251332603554831050927/125"
    ],
    [
      "3632416294213",
      "-2273712679048294915"
    ],
    [
      "62144915370822013/3481",
      "-14438096208143119447004681/205379"
    ],
    [
      "1633075507096888541/7225",
      "-2085936826191907178827290119/614125"
    ],
    [
      "87995534283422269/9801",
      "-19787883532142566354031249/970299"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization at T = -568/1107 of the rank-11 fibration of X163 described by wgxli for ICARM #718. Independently recovered polynomial sections and rational-point search yield 18 points with an exact independence certificate, proving rank >= 18.",
  "created_at": "2026-09-18 01:22:54",
  "updated_at": "2026-09-18 01:22:54"
}