{
  "id": 4153,
  "curve_key": "21152542162056931827225:-2409349378149845744497531046704125",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-440677961709519413067",
    "2788598817413231694706929675841"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "naive_height": 154.21814114379526,
  "faltings_height": 10.86414829774099,
  "conductor": "6406598481347583107040288514590005345008277552765149950",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "61",
    "2687",
    "20530287101",
    "19897798396246051",
    "12507442668704146019"
  ],
  "discriminant": "2117661086768935173637748366694510079259079843331815533785312500",
  "regulator": "27526513317919953.2827353053250146371864109614989835272606640544299450632",
  "points": [
    [
      "-8568833376",
      "2436298409410913"
    ],
    [
      "67965106524",
      "16934725544619763"
    ],
    [
      "91941247349",
      "-27193229354194462"
    ],
    [
      "16920443240",
      "420085526521799"
    ],
    [
      "17547949178",
      "-677617409368441"
    ],
    [
      "116528224184",
      "39163110389252183"
    ],
    [
      "-3929034576",
      "-2111723403631487"
    ],
    [
      "-6924646926",
      "2346936823163363"
    ],
    [
      "158154382291/9",
      "18532615233972926/27"
    ],
    [
      "165019649559",
      "66511556658431183"
    ],
    [
      "529774093604/25",
      "215280378210426607/125"
    ],
    [
      "7147203578",
      "63878154336863"
    ],
    [
      "-2573238189/4",
      "14021300488864589/8"
    ],
    [
      "1578176722444/81",
      "-921790708192789973/729"
    ],
    [
      "-191340658628/9",
      "-43099096123316309/27"
    ],
    [
      "3285573923906/169",
      "2752230452523045311/2197"
    ],
    [
      "-210075335587/16",
      "-160780413217630453/64"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Mestre construction: sextuple [-217, -205, -48, -7, 237, 240], T = 127; y^2 = r(x) with p(x-T)p(x+T) = g(x)^2 - r(x). ",
  "created_at": "2026-10-11 17:17:16",
  "updated_at": "2026-10-11 17:17:16"
}