{
  "id": 6281,
  "curve_key": "991881249839012200382309983773254272:-987528351447432100898638694799787650642948969430098304",
  "ainvs": [
    "0",
    "1",
    "0",
    "-20664192704979420841298124661942797",
    "1142972628990083443226100921025132463367001234711311"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 248.65473438329775,
  "faltings_height": 18.454891732416637,
  "conductor": "163293419186021457311442065268233444059774956",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "17",
    "23",
    "31",
    "41",
    "47",
    "73",
    "197",
    "359",
    "389",
    "757",
    "15289",
    "15661",
    "51631",
    "26202601"
  ],
  "discriminant": "363837833876940970796652327466105848631057271363958317492930530659553474644209322264976195485295858944",
  "regulator": "548270053118500.32898562470233221507584900159877903813806040854",
  "points": [
    [
      "141762755028462020277282/674041",
      "-43221038925952571393338671816330453/553387661"
    ],
    [
      "63297284513897925225617138/718293601",
      "-48366355064067462330952137130334387271/19250986800401"
    ],
    [
      "20517791865065917030221/198916",
      "-926002151924048681981820294192051/88716536"
    ],
    [
      "45807117630438879974457/436921",
      "3278776925061854523384438244876902/288804781"
    ],
    [
      "31526319270692823474854340091605083265/38467701021150069601",
      "-174457250010737457339913308029963877577336890782809087266/238585665903213922285307383151"
    ],
    [
      "18708626961632793597161/177241",
      "-876057667934067648610877798452314/74618461"
    ],
    [
      "3690780603305263462445853/1471369",
      "-7079112262502171882111625574741044114/1784770597"
    ],
    [
      "2071043844002815888413/14641",
      "57415214563938663901574680710954/1771561"
    ],
    [
      "18371133354000003075475370/1247689",
      "-78737805061710541688672862897856184913/1393668613"
    ],
    [
      "50639914218086934516570106890/435387505921",
      "-5082306772543591238418135931625837282861979/287285656519406719"
    ],
    [
      "2917571726659298213466/32041",
      "23185999233521682366251883670569/5735339"
    ],
    [
      "354548354410405373152995320409/3983309447329",
      "-23656773622583602941391343624850374166165042/7949980611096506767"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "Voznyy (2026), T = 10728/329 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 23:40:32",
  "updated_at": "2026-10-31 23:40:32"
}