{
  "id": 333,
  "curve_key": "1146773049056886892421413909825:-1226535449840741492541734838493470079803270625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-23891105188685143592112789788",
    "1419601215093448810627501450420291027410192"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 207.64351423072654,
  "faltings_height": 15.084782412420235,
  "conductor": "131944541736270829990525135723297231720924027431424328761515243063150",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "7262584531",
    "112718068888168147",
    "4862091821681746797837190485335157793"
  ],
  "discriminant": "2152056942700264818719027733126048402613339655450827996023631575722662975639296000000",
  "regulator": "4670728444081471861.943611114955809605351027382415234272937662712114695647415",
  "points": [
    [
      "802902135464363935216/383161",
      "-22690438940309708009086818304124/237176659"
    ],
    [
      "56461682270968648/49",
      "-13301264929026283654416068/343"
    ],
    [
      "657778911301236",
      "-16441039657074125259720"
    ],
    [
      "6389931597586262770168/48344209",
      "-253987993652797540416741022787452/336137285177"
    ],
    [
      "79458746926432",
      "-151400256741193904516"
    ],
    [
      "303353716555143808/5329",
      "-192184625435335240210079492/389017"
    ],
    [
      "41819388286822169272/9628609",
      "-34273604901646813278927449051300/29877573727"
    ],
    [
      "-28753310689333592/289",
      "-8238231047207775899063068/4913"
    ],
    [
      "1296812620898148032452/591361",
      "46586890441260864333635548737256/454756609"
    ],
    [
      "1212499903017749954887/401956",
      "42166051189094922213739956445321/254840104"
    ],
    [
      "12159610562402775448/3721",
      "42354737018869119585461129140/226981"
    ],
    [
      "10408742863846012/121",
      "41745309263217658764284/1331"
    ],
    [
      "1629610964813174842297/19571776",
      "-7545777660739706787143667423439/86585537024"
    ],
    [
      "1621227152774785151669062/36808489",
      "2064253984470696842385038065304576800/223317102763"
    ],
    [
      "207286518328532752",
      "-94374891488025371096746076"
    ],
    [
      "90988414437426738568/9409",
      "-867808711921688565975679471148/912673"
    ],
    [
      "266709390008921947688965072/3103301501161",
      "182854778168590565026065125486615701516/5466834887173739659"
    ],
    [
      "20751533335921432",
      "-2989257151328889938221916"
    ],
    [
      "1286971669361752",
      "45850610626306355032324"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": "New in this search: Mestre quartic family with roots [0,115,206,234,731,784], T=823/24. 19 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [10000000,10000].",
  "created_at": "2026-08-24 19:17:59",
  "updated_at": "2026-08-24 19:17:59"
}