{
  "id": 5953,
  "curve_key": "36788636867114542914222963103220481:-6563677158638729884045496687909174211338333874816129",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-766429934731552977379645064650427",
    "7596848563239270890734215960560899682108411851051"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 238.77149125653258,
  "faltings_height": 17.853503975252085,
  "conductor": "23854930784364955283661844396465787210564790",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "29",
    "43",
    "53",
    "71",
    "101",
    "397",
    "853",
    "10597",
    "50077",
    "36338257",
    "104569453"
  ],
  "discriminant": "3881957860761395376634126157272771955059123310403123174465850644045024381322345956770304000000000000",
  "regulator": "1006687040041661.7923992456051805707037850221965975289942282228",
  "points": [
    [
      "27661320261852082790851/1142761",
      "-2194611372267905699149149456567454/1221611509"
    ],
    [
      "33623345946156894287399192299/1700043076449",
      "927058548985483240874935997504087511047482/2216613065529563793"
    ],
    [
      "374559068559670777279171/18139081",
      "-58597756947706132285610470230799394/77254345979"
    ],
    [
      "1799234741094505018147291951/5435523076",
      "76059468638589390882751978208801424929549/400739374301176"
    ],
    [
      "2238100739735725829611/93025",
      "-49823182146927615348520345553606/28372625"
    ],
    [
      "343387284587475406682028691/17273582041",
      "1057078577365420562605735220468032271986/2270249614066589"
    ],
    [
      "47339976195043587653930279611/2093898714961",
      "-4093495898174391890960296719008720430057866/3029936351408730791"
    ],
    [
      "3512351448396158688659/2809",
      "-208109218787867865732241014873902/148877"
    ],
    [
      "2126318187695233017533669179/44595725329",
      "-83942141366808104646893045472287733747958/9417591487802233"
    ],
    [
      "258616370954129519740139/5678689",
      "110888372139986084604050712555869638/13532315887"
    ],
    [
      "126874277576240900168467736611/6486093461961",
      "4938490671680167775177598845230806808941634/16518659593146497541"
    ],
    [
      "125925122188201846653980345895179/1227146929851649",
      "-1365837775408947636168941168588226092805467880038/42987763188236177003393"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-10-26 10:49:44"
    }
  ],
  "commentary": "Voznyy (2026), T = -9985/1638 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": "2026-10-26 10:48:52",
  "updated_at": "2026-10-26 10:49:44"
}