{
  "id": 342,
  "curve_key": "66794547105633374274601817479825:-546253287876463638153044596585872992436315085625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-1391553064700695297387537864163",
    "632237601708869371752246880018016126067921281"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 219.8388239002391,
  "faltings_height": 16.077844519792375,
  "conductor": "25582449424667650913572690219204060112186535917088135557790710631313352389050",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "10982045197",
    "130503054599564132532868602134756795265311693363089881885691589"
  ],
  "discriminant": "-224544518159358460458242318645476296228674299566935193705566332442671710143907131904000000",
  "regulator": "127836638655370553024.8093793090760805015496216256853242770719472002102863646",
  "points": [
    [
      "222580170941029009509963915/1216609",
      "-3320700499005602098592328210951318215686/1341919727"
    ],
    [
      "15997794013166186205/1681",
      "-63516948951917242882076286538/68921"
    ],
    [
      "24523399592876245268555/4116841",
      "-3770151461228919948964463677342042/8353070389"
    ],
    [
      "63608988183595951879/18225",
      "-481451301097855542258628700278/2460375"
    ],
    [
      "2412659329425315",
      "-106389865484273319795458"
    ],
    [
      "29935033694463679/225",
      "71551113611155031077107062/3375"
    ],
    [
      "699522691224164861327035/2296038889",
      "1692150122388151296454402555985151446/110019295444213"
    ],
    [
      "629988782486369715/961",
      "39119259381717047125170322/29791"
    ],
    [
      "357793325662813235/529",
      "8219560419083748633332914/12167"
    ],
    [
      "5136391303343585155/6561",
      "2528720778321622076503960702/531441"
    ],
    [
      "931443977980185",
      "12008054729918060563432"
    ],
    [
      "4636434350273393695/1089",
      "9634954864148332440193362614/35937"
    ],
    [
      "4647240686381935",
      "307459095765403595866682"
    ],
    [
      "80483979169908302084449415/1351738756",
      "-721904184596216915316984299158925280143/49698027103096"
    ],
    [
      "37629837485889561389035/56385081",
      "376744110291641780530902051184678/423395573229"
    ],
    [
      "1349983754625485038489/151321",
      "49188018416713726738684244643472/58863869"
    ],
    [
      "19313638877029794697035/4044121",
      "2608940737441192802891687337307642/8132727331"
    ],
    [
      "8476247175871114835/361",
      "-24647181211649950105309929062/6859"
    ],
    [
      "9171897417206983035/11881",
      "5502037771750027411464464278/1295029"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": "New in this search: Mestre quartic family with roots [0,115,206,234,731,784], T=9693/14. 19 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [10000000,10000].",
  "created_at": "2026-08-24 19:19:09",
  "updated_at": "2026-08-24 19:19:09"
}