{
  "id": 6394,
  "curve_key": "790074736643333560690332001:-22209624462683532989046390565200369498001",
  "ainvs": [
    "1",
    "0",
    "0",
    "-16459890346736115847715250",
    "25705583868845310042756279588957562500"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 185.80268871210453,
  "faltings_height": 13.175800494545111,
  "conductor": "12179989966747952083343629383030",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "19",
    "103",
    "181",
    "233",
    "337",
    "613",
    "661",
    "1567",
    "3307",
    "21523"
  ],
  "discriminant": "-51201457123182158038594651768591235679362288296412968225443938304000000000",
  "regulator": "96791469475.26889431196396536293886668006564998787209539265",
  "points": [
    [
      "60481077998682507300/24334489",
      "46341335566966125403027815750/120042034237"
    ],
    [
      "211900819777873393140/90801841",
      "46076382612194601397978119150/865250742889"
    ],
    [
      "1017552185497059300/466489",
      "135326783610311577508028250/318611987"
    ],
    [
      "129865786779500/49",
      "-286561456731784780750/343"
    ],
    [
      "14730756837355140/6241",
      "33362588700859187152290/493039"
    ],
    [
      "5870940705540",
      "11464280888564842110"
    ],
    [
      "4704604551380924302500/1728979561",
      "74165987417148105549636624297750/71892699125941"
    ],
    [
      "61511842627544562660/37687321",
      "-413121319562918949910350576390/231362463619"
    ],
    [
      "160759522821012750/2209",
      "-64358171327837955851136000/103823"
    ],
    [
      "11271927448948514330177910/4829142495961",
      "559366579047409201522292497981588440/10612190338291672291"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "Voznyy (2026), T = -225/136 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": "2026-11-02 01:16:01",
  "updated_at": "2026-11-02 01:16:01"
}