{
  "id": 1375,
  "curve_key": "371489095690826134936512064:-7160100217090418905129859102530495017472",
  "ainvs": [
    "0",
    "1",
    "0",
    "-7739356160225544477844001",
    "8287153029037256910365409890880643455"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2
  ],
  "naive_height": 183.5386852304199,
  "faltings_height": 12.764352036662743,
  "conductor": "23354778245864734004307533064634560",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "23",
    "29",
    "31",
    "41",
    "43",
    "53",
    "61",
    "71",
    "97",
    "101",
    "103",
    "113",
    "139",
    "181",
    "373"
  ],
  "discriminant": "638893263333002723265169980004644396987249666267748099994354531205120",
  "regulator": "134626083002.675186460383627562439976572126426296192064131948",
  "points": [
    [
      "1609505127706",
      "-7315144083743001"
    ],
    [
      "9987971523949/4",
      "17028390609735369117/8"
    ],
    [
      "1644172380205",
      "83744939811919980"
    ],
    [
      "1606348921261",
      "251504274001836"
    ],
    [
      "80282577888361/49",
      "24361862809964350488/343"
    ],
    [
      "1606762507705",
      "1263605161316520"
    ],
    [
      "1607623205389",
      "3174135744131484"
    ],
    [
      "1609877413609",
      "8133562893747984"
    ],
    [
      "1260408411271249/784",
      "71643280907786986497/21952"
    ],
    [
      "7797665315641",
      "-20544202220547749304"
    ],
    [
      "3575504677066",
      "5130802690850493921"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Obtained from curve #1202, submitted by Noam Elkies, which has rank at least 11 and torsion \\(\\mathbf Z/2\\mathbf Z\\times\\mathbf Z/2\\mathbf Z\\). Quotienting by the rational 2-torsion point \\((-803153556053,0)\\) gives the 2-isogenous curve \\(y^2=x^3+4818921336316x^2+1311454974983248973284x\\). Its global minimal model has ainvs \\([0,1,0,-7739356160225544477844001,8287153029037256910365409890880643455]\\), torsion \\(\\mathbf Z/2\\mathbf Z\\), and conductor \\(23354778245864734004307533064634560\\). The eleven independent points on #1202 were mapped through the 2-isogeny, giving eleven independent points on the quotient. The isogeny, minimal model, conductor, torsion and image points were verified in Magma.",
  "created_at": "2026-09-24 18:38:24",
  "updated_at": "2026-09-24 18:38:24"
}