{
  "id": 1177,
  "curve_key": "10975233684025722425576161:31298277164157149906728788374943002159",
  "ainvs": [
    "1",
    "0",
    "0",
    "-228650701750535883866170",
    "-36224857828904644394970864535395100"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    6
  ],
  "naive_height": 172.9730504489574,
  "faltings_height": 12.404889658318028,
  "conductor": "138952056675401970",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "47",
    "59",
    "73",
    "347",
    "3467"
  ],
  "discriminant": "198175867991574047099960189533269983628883789627406319353856000000000000",
  "regulator": "85663.5297982189326679822086603706427880721874797",
  "points": [
    [
      "-188273633260",
      "-12260101833183370"
    ],
    [
      "-302322033160",
      "-72590985215112970"
    ],
    [
      "-780084462475402060/3575881",
      "-386901269091276775587352270/6761990971"
    ],
    [
      "-8734244133188131660/39702601",
      "-14650410569124913791792984370/250166088901"
    ],
    [
      "-8633487293135560/36481",
      "-474254713514290896305270/6967871"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by computing a rational isogeny from curve#1088 and mapping all 5 independent witness points to the global minimal model. Isogenies preserve the Mordell-Weil rank; the image points are independently certified by the site verifier. Torsion computed exactly with PARI/GP elltors. Conductor is unchanged by the isogeny.",
  "created_at": "2026-09-23 21:38:27",
  "updated_at": "2026-09-23 21:38:27"
}