{
  "id": 329,
  "curve_key": "795639199102776779440116220435825:-22461264350222105705843579561608957207578454495625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-16575816647974516238335754592413",
    "25996833738682985808506465614332304868873612531"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 227.27175340972093,
  "faltings_height": 16.70589866485531,
  "conductor": "5828132005406968037770167747623110174516223438517658736647919417759236327050",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "426969377685492163939206428397297448682507211613015292062118638663680317"
  ],
  "discriminant": "-483551538222869881998543760521303109946455701683075824214473152684439136068904191524864000000",
  "regulator": "361042181815555790913.512234502128084081606251076656609566935927822537576899009",
  "points": [
    [
      "444226461849009989",
      "-296065949383519030947500162"
    ],
    [
      "285316058376951015/4",
      "-152158536738701474857563469/8"
    ],
    [
      "119948689485761235/4",
      "-41178103173156145618059139/8"
    ],
    [
      "-2600566741471505035/1849",
      "17149942716363680891855292674/79507"
    ],
    [
      "-1047756134226289785/2401",
      "21419596332849183712776397108/117649"
    ],
    [
      "6606816863449317922415/3087049",
      "97697485068772354526551877032276/5423945093"
    ],
    [
      "154331319852866995221615/67683529",
      "4172064379956401387412803727850156/556832393083"
    ],
    [
      "1685893605317875332297095/683142769",
      "195684949471868387133315863502268516/17855302553353"
    ],
    [
      "2639383489477751",
      "25174459314881264520260"
    ],
    [
      "5473774756283255",
      "315072903426741416712772"
    ],
    [
      "31829441734598323671591/5564881",
      "4515340891762404777388628704359772/13127554279"
    ],
    [
      "31803966046307764695/2209",
      "172850329505832067944832604156/103823"
    ],
    [
      "70762535775867854329731315/2761817809",
      "588160406423278154128372064271293658764/145141811316377"
    ],
    [
      "5046012642789497815/2209",
      "750376678488493308648266236/103823"
    ],
    [
      "21941200566705822735/3481",
      "85161072051876567529822795628/205379"
    ],
    [
      "12520520947667379008285415/19737159121",
      "347847058560646447485602806930667208548/2772853747750169"
    ],
    [
      "229390313215511415",
      "109848634975296087867636292"
    ],
    [
      "14389525428316005",
      "1663415579976555228142972"
    ],
    [
      "559636820498128952795015/78961",
      "-418657956462293055019116465358819228/22188041"
    ],
    [
      "398951755860475915147535/1388382121",
      "7542574120221595966297871610549980692/51732506210581"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": "New in this search: Mestre quartic family with roots [0,115,206,234,731,784], T=22841/32. 20 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [100000000,50000].",
  "created_at": "2026-08-24 19:17:37",
  "updated_at": "2026-08-24 19:17:37"
}