{
  "id": 6012,
  "curve_key": "385653423742713454018209340810308663424:-7575609977796288784717534767755318225411272865336515754368",
  "ainvs": [
    "0",
    "1",
    "0",
    "-8034446327973196958712694600214763821",
    "8768067103930889794448627575577589700581037986660490479"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 266.54456834787135,
  "faltings_height": 19.941044953940185,
  "conductor": "3137286081662052951736824389966369871339603060",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "31",
    "43",
    "251",
    "313",
    "1669",
    "111853039",
    "266840807022416443"
  ],
  "discriminant": "-18626685254328311914143810766405568877304075267592872372004638589820948744752347192470397250246603277406636800",
  "regulator": "2536455792934374.9998154082436497579633575076777518072398858634",
  "points": [
    [
      "3679106932009049260613728818947506909/2259441490912289161",
      "-179296227430770070242356317278480781039553282913730590/3396265624429026669112303909"
    ],
    [
      "100218441800874715593683665123381/19573968649",
      "1003278262027562879471494906184509534324805094930/2738535231775643"
    ],
    [
      "5471640919457564786613216169/839608576",
      "371502168014208077780298194169869042580885/24328498098176"
    ],
    [
      "219397935853563571472846898086783461/149682675064733209",
      "21716252547687719385058979815364531191561160352234690/57910498596696306087735677"
    ],
    [
      "1302702600340800350023021619726701/782727916425625",
      "1734899413213191962229397797908044776808280293074/21898594168016727671875"
    ],
    [
      "1378944915973238297082466/769129",
      "-239730016646097512431784416184891235/674526133"
    ],
    [
      "-39565978369743147014230691471/12472422400",
      "-2127044529624221216670382602912193591195767/1392920133632000"
    ],
    [
      "20767650197060885581309309/12602500",
      "-2490145525992744124789374032391075627/44738875000"
    ],
    [
      "408794450539375437912621070141/5055494404",
      "261212588637503460548881412377635677640428085/359455763113208"
    ],
    [
      "1679281815620119625401/1369",
      "-44109500136619274490017230035690/50653"
    ],
    [
      "2766374744244254035006415696568608989/60560511549926116",
      "4592496529502406488866735143193616046848560664285251605/14903363781793561552896664"
    ],
    [
      "-1439712138781744102424819/1216609",
      "5470472522014909398842743616305990410/1341919727"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "Voznyy (2026), T = -10272/3553 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": "2026-10-28 02:18:27",
  "updated_at": "2026-10-28 02:18:27"
}