{
  "id": 335,
  "curve_key": "5263126383854955044328934641201:-12814178321569496047711995998255735255531301801",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-109648466330311563423519471692",
    "14831224909223981171042503872168327240436559"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 212.33376284800775,
  "faltings_height": 15.640201224351143,
  "conductor": "26131480673084455535055442121869459110183352891317952147665051014474190",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "71",
    "2223291744473",
    "81117610011058082651461",
    "121257874715182550773823852011"
  ],
  "discriminant": "-10655056235250006421362330734062242646577351173136784942681626012228895953862213427200000",
  "regulator": "10713426441429307164.08685871875394308560929749321424630343268659017739686607",
  "points": [
    [
      "221608685343698629923/41209",
      "-3292881277111888095288314573803/8365427"
    ],
    [
      "490362676990797693/169",
      "-341242384963643848709435783/2197"
    ],
    [
      "233965481556897073/169",
      "-110209435812361409670530723/2197"
    ],
    [
      "1115362331312277",
      "-35778222258987515923019"
    ],
    [
      "1407589819737983959881/1530169",
      "-49805952524110440557323347536579/1892819053"
    ],
    [
      "-5188162901069531283/72361",
      "91969830766048396031072701049/19465109"
    ],
    [
      "59467225364789816623/368449",
      "258743453724598266929113530363/223648543"
    ],
    [
      "210266770728117",
      "1035439221889299277141"
    ],
    [
      "436374416467848621/1849",
      "115182735830651444642458351/79507"
    ],
    [
      "462536637767410249437/1394761",
      "6366728134940215445202805472681/1647212741"
    ],
    [
      "778679660054993691/1225",
      "609331599371070275349844559/42875"
    ],
    [
      "161234648327618978187/28561",
      "2043888117571704073572039203269/4826809"
    ],
    [
      "48416703022599357",
      "-10653264032295390235339259"
    ],
    [
      "6593806095211503381/139129",
      "161968109309531435841565562881/51895117"
    ],
    [
      "148833567463192797/16",
      "-57382571347653779996094101/64"
    ],
    [
      "117559475102469",
      "1888308117378624822037"
    ],
    [
      "35158120425305467/196",
      "2652541571506819465114179/2744"
    ],
    [
      "23865502012886843668533/113569",
      "3686848755353665471988237369207653/38272753"
    ],
    [
      "161019268615172093628027/3818116",
      "64610548578070432026379876694050729/7460598664"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": "New in this search: Mestre quartic family with roots [0,115,206,234,731,784], T=5015/22. 19 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [10000000,10000].",
  "created_at": "2026-08-24 19:18:32",
  "updated_at": "2026-08-24 19:18:32"
}