{
  "id": 5866,
  "curve_key": "270623329926140127797796551118347878681:-4451681707950178992203962821318506906618546487551907879421",
  "ainvs": [
    "1",
    "0",
    "1",
    "-5637986040127919329120761481632247473",
    "5152409384201596055321791465774648975603994977863872756"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 265.4813738260492,
  "faltings_height": 19.800537450854176,
  "conductor": "581459793254966336566732749789261962353630126730",
  "bad_primes": [
    "2",
    "5",
    "7",
    "23",
    "29",
    "31",
    "37",
    "41",
    "43",
    "61",
    "101",
    "181",
    "1249",
    "1373",
    "3727",
    "85247677",
    "166167293059"
  ],
  "discriminant": "1254158389340923198127704514778979327874655786743780209366406136942795241891565868290465098674580566406250000",
  "regulator": "5148217095823413.0356775419879002538795452750984118211688952248",
  "points": [
    [
      "1711609172912887431468355495/294774561",
      "-65633842731339752707412393028704484684482/5060984437809"
    ],
    [
      "2316521638686697795",
      "2126729670137785265736651102"
    ],
    [
      "2880683613961887161907708295/2054446276",
      "-5720599214592964269183906628307605980073/93119831905976"
    ],
    [
      "1852142070274200397984165195/295461721",
      "74665576663727131559631987195543145790438/5078691522269"
    ],
    [
      "1549960160952537625043455/94249",
      "1910569840056534696670649481394206186/28934443"
    ],
    [
      "19030966014390119354747707312595/12925973563441",
      "9643749398956519809212686473306584070561587122/46472377899406087511"
    ],
    [
      "30109992590741616822755794395/21322132441",
      "256560670745641804607825115661199328845822/3113479101167261"
    ],
    [
      "150810791515265553135716001980/103064755369",
      "-6243089641212891793045376462137503834195769/33087599869397653"
    ],
    [
      "2007345513017347986007170462239/1454612081329",
      "-13550594453642125734812361156893769410736502/1754368356764711017"
    ],
    [
      "17360202434018790584827101980/12146905369",
      "157810275441064934092730411869752200905144/1338746881433597"
    ],
    [
      "16835872119900433822277227945895/6501434143681",
      "46645798122125846263268253749263043991510429442/16577298266650520671"
    ],
    [
      "9386174271786239019480976985795/5554501526401",
      "-8786772290351399278282584205962045883148010302/13090843642920350399"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "Voznyy (2026), T = -3559/4025 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": "2026-10-25 16:41:21",
  "updated_at": "2026-10-25 16:41:21"
}