{
  "id": 1147,
  "curve_key": "1472751839641353561393352717456:-436867670338004943676364816352355270261943104",
  "ainvs": [
    "0",
    "1",
    "0",
    "-30682329992528199195694848280",
    "505633877706014012922832139156234849705600"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2,
    2
  ],
  "naive_height": 208.39405632108048,
  "faltings_height": 15.430678418047613,
  "conductor": "1128310354841987032068083640",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "31",
    "41",
    "53",
    "61",
    "67",
    "109",
    "257",
    "263",
    "6857"
  ],
  "discriminant": "1738161114326106750283883934756093697745475788190052358222531735838813272941107600000000",
  "regulator": "233557909.634031665003976922249867242089139925297950721",
  "points": [
    [
      "-32182203519760",
      "1208192014418530050000"
    ],
    [
      "-9538996003285",
      "892997494010708936850"
    ],
    [
      "-2235318896624560/121",
      "-1374315135119784722685600/1331"
    ],
    [
      "-83224318109345110040/1912689",
      "3507618465482873224340109725200/2645248887"
    ],
    [
      "-144952105945360",
      "-1381121698192868948400"
    ],
    [
      "-1258574332119440/9",
      "-38767370545383228557200/27"
    ],
    [
      "11084743961228840/10201",
      "-708060992417925152410731600/1030301"
    ],
    [
      "522607806485744",
      "-11278514444719522094640"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by computing a rational isogeny from curve#1108 and mapping all 8 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 21:37:34",
  "updated_at": "2026-09-23 21:37:34"
}