{
  "id": 1164,
  "curve_key": "173837967547706258173456:-213866940106345967100745162076039104",
  "ainvs": [
    "0",
    "1",
    "0",
    "-3621624323910547045280",
    "247531180677433957517892273758100"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4
  ],
  "naive_height": 162.701324230478,
  "faltings_height": 11.611917762204328,
  "conductor": "104034096695931795120",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "29",
    "37",
    "41",
    "137",
    "191",
    "557"
  ],
  "discriminant": "-23429251998509983442800459090756176772012672758021427375209987840000",
  "regulator": "11348194.14970519083630702006996408532292227619385686",
  "points": [
    [
      "15026989060",
      "14017928591500470"
    ],
    [
      "323732430301/4",
      "176099483358436365/8"
    ],
    [
      "33809593765/4",
      "117989459575942815/8"
    ],
    [
      "4313759983645/4",
      "8946428798888827155/8"
    ],
    [
      "429279161047885/13924",
      "21116633831031785228325/1643032"
    ],
    [
      "-2886663947900/49",
      "5492609911683509670/343"
    ],
    [
      "-81560718260",
      "599389355032650"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by computing a rational isogeny from curve#1089 and mapping all 7 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 21:38:04",
  "updated_at": "2026-09-23 21:38:04"
}