{
  "id": 5954,
  "curve_key": "169199097209283681696568507145257996161:-2201008947552808105603321343713162888181483334520250027841",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-3524981191860076702011843898859541587",
    "2547464059667601974959163519855253999787085204483693299"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 264.0725323368366,
  "faltings_height": 19.6843792295097,
  "conductor": "9540524621154266900569830906607102382329164090",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "37",
    "149",
    "223",
    "283",
    "293",
    "613",
    "27487",
    "177787",
    "612583",
    "2998252970539"
  ],
  "discriminant": "-319465164959143229842920421177179570129081779373334332207791466547301885006700661068529506025734144000000000",
  "regulator": "28251256440676416.042089829499206966906511684895427355824009085",
  "points": [
    [
      "12760590949039390694604465763/9692993209",
      "-414334095338912830552064168001078134689958/954304260405677"
    ],
    [
      "-55904098852840974838830931573/87923517361",
      "-55499330796103270720157750228502973608491986/26070993444366359"
    ],
    [
      "5067200076952064774708027/5612161",
      "4221770941686571581635146566923493314/13295209409"
    ],
    [
      "7667348508113360020434067/7070281",
      "227071526570733200075855483009391734/18799877179"
    ],
    [
      "115915383412896405852314132867018827/88518965011634161",
      "11080514879533349282741156651748315029619815760839314/26336283652724496507886409"
    ],
    [
      "-76855956265554349611869/822649",
      "-1265359785006847766230662342667945114/746142643"
    ],
    [
      "-284202805762907722024944877757/137572002649",
      "51358664329805495256922511562168019420343878/51026418786532643"
    ],
    [
      "-26177651889790186715665037117/13059232729",
      "1863308008277591969977229986738020819861818/1492369938571933"
    ],
    [
      "3472412303699687139724376130883/318306970969",
      "6380526016229326739013097614693684168240160838/179584655030087203"
    ],
    [
      "803595003037040070543296491/625250025",
      "5850420540440019617332503373085861040146/15634376875125"
    ],
    [
      "923331021523599387366592588363/732912346609",
      "204407569801181805380319120511393039207768942/627448458669004727"
    ],
    [
      "1005446022721576165984586214476083/858438256979689",
      "-4022810264951221049817661458191407675332087187222/25151482928523974634613"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "Voznyy (2026), T = -10375/3108 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 10:55:07",
  "updated_at": "2026-10-26 10:55:07"
}