{
  "id": 6274,
  "curve_key": "2543317022626598219884294906177211425:-4134743487000110326542295267438559971263281405351324593",
  "ainvs": [
    "1",
    "0",
    "0",
    "-52985771304720796247589477212025238",
    "4785582739583461021675138580438266946107452599636004"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 251.5180406272942,
  "faltings_height": 18.853417132173348,
  "conductor": "12079050599388792997553643082553593819574810818",
  "bad_primes": [
    "2",
    "7",
    "13",
    "23",
    "37",
    "61",
    "67",
    "101",
    "349",
    "373",
    "563",
    "788268211",
    "3270311898781134307"
  ],
  "discriminant": "-373122405758427398148345731160332326786195546704476603384033993153830621350549458406541519927788760465408",
  "regulator": "725913829766315.07924905774027253424830146759526629214699064298",
  "points": [
    [
      "8839478258221293287388190086166916/63044346619386889",
      "168134491166345274216952788889871036447618234525866/15829573809042800667288037"
    ],
    [
      "110078742939144285604004876/533379025",
      "633009226017990638785807628725835828214/12318388582375"
    ],
    [
      "88943025043239659963239244/779135569",
      "325910500429721932799389088533410083082/21748011137497"
    ],
    [
      "24911055265561082358390780/910047889",
      "1590331494569999519077206419224594180326/27453414667463"
    ],
    [
      "11503114232260523524675244/78340201",
      "-9074134133729759406224450321555444322/693389119051"
    ],
    [
      "72932732028303737057701116/587238289",
      "-156303155622768623400651155510512315254/14230545457337"
    ],
    [
      "105971641744033279617176457580/162475904889",
      "-32593855147358287557938442512675059773903826/65491275170372787"
    ],
    [
      "-518360932820866915901028763668020/7926393783908209",
      "-63004246290036657203281383710199201882626352946454/705689192720301668008073"
    ],
    [
      "-366234237513854792519897116/4382042809",
      "26947851810940875397865293687065821499314/290078087827373"
    ],
    [
      "3709742285582753513612816484364/12400588973809",
      "5472960219349186870654268394222325679026714518/43668016840052781623"
    ],
    [
      "162402399689824662156609820844/1217502594025",
      "-12829595597055269357962515130997757303389982/1343398449760155125"
    ],
    [
      "12341835637118909293528975065676/149460967528929",
      "-57005572411743608245289664438056429163444123194/1827223550030421761967"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "Voznyy (2026), T = 4741/1924 for the rank-5 fibration of X163 given by y^2 + (9T^2 - 6T + 244)xy + (13T - 90)(22T - 15)(5T + 6)(4T + 15)y = x^3 mentioned in the curve#4645",
  "created_at": "2026-10-31 23:35:38",
  "updated_at": "2026-10-31 23:35:38"
}