{
  "id": 330,
  "curve_key": "23178534088209847884249390419344:-111348432312098510936374116025385650698319009472",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-482886126837705164255195633736",
    "128875500361225289360623432042214069669747136"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 216.6623381560879,
  "faltings_height": 15.857788812622744,
  "conductor": "76112461196808026563075717934065940819332588227906251909576775948240",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "31",
    "37",
    "61",
    "1132627",
    "2771315443373",
    "58061085533848247634531022486933677533"
  ],
  "discriminant": "31287757709910264613757109283395755219056531022112192673139216897563002547901499488793600",
  "regulator": "1521972441335808431.928851598137744911238709585530506718258709695380672789941",
  "points": [
    [
      "2290804687204732584/25",
      "-3467126139839410434496670952/125"
    ],
    [
      "14577958168095021",
      "-1758167039920555817686650"
    ],
    [
      "56016686080303825/9",
      "-13178617360573382520013288/27"
    ],
    [
      "-657295472815786776/1849",
      "1271147590336516660872452040/79507"
    ],
    [
      "-306471756195812010/2401",
      "1614978607764236363908820814/117649"
    ],
    [
      "691151498047146860753/2042041",
      "5987426964310655713564791841996/2918076589"
    ],
    [
      "33337411143611276768508/87965641",
      "453783752815879059182557725526596/825029746939"
    ],
    [
      "383446365856044",
      "-305150462427497032500"
    ],
    [
      "10994356009984432186257/25080064",
      "150382639071347861191995229169607/125600960512"
    ],
    [
      "494012030343406",
      "3299475131381881330830"
    ],
    [
      "1220418581612028",
      "36841145344897523404236"
    ],
    [
      "63381732662543522016246/49434961",
      "13978323337335148903175525789893950/347577210791"
    ],
    [
      "-515788542746545644644346/11161288609",
      "14494136715613833223569847065569193390/1179156657675023"
    ],
    [
      "16506961344829371228919884/7211915929",
      "64277291605080054680070367599590751900/612457536438467"
    ],
    [
      "588440415263721921086/1530169",
      "414860888817657392198431091210/1892819053"
    ],
    [
      "874515181660886139644/26569",
      "25855623015409995950200727146940/4330747"
    ],
    [
      "2336385763075826094709029/6228682084",
      "354966584859075458936360848632239685/491580047433448"
    ],
    [
      "1712362799748476",
      "65749266927887199760180"
    ],
    [
      "19624507648156935696/17161",
      "73609385995203769256077362600/2248091"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": "New in this search: Mestre quartic family with roots [0,115,206,234,731,784], T=4287/7. 19 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [100000000,50000].",
  "created_at": "2026-08-24 19:17:42",
  "updated_at": "2026-08-24 19:17:42"
}