{
  "id": 1377,
  "curve_key": "14650048978039507247007167521:-1773203643260773860827263717372929354229681",
  "ainvs": [
    "1",
    "0",
    "0",
    "-305209353709156400979315990",
    "2052319031551796164066894280222290328100"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4
  ],
  "naive_height": 194.56272356852284,
  "faltings_height": 13.392008762501876,
  "conductor": "3985472961137327010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "29",
    "31",
    "43",
    "173",
    "257",
    "367",
    "953"
  ],
  "discriminant": "96010560714044258693986173065625600000000000000000000000000000000",
  "regulator": "78354045.9062285649286047818538931300307983312688",
  "points": [
    [
      "7899305616504722267724/783160225",
      "-111134593729620941915095302/21916738896625"
    ],
    [
      "18096668989437231425435435436/1794156535525225",
      "-566697509437646847022180756522013214/75995958541161685059125"
    ],
    [
      "584407629884600769978739949267020/57939878506167457569",
      "-2479226236479772715276940765046029462634630/441028210669438677673584616497"
    ],
    [
      "1419002035305293792238082716/140683676830225",
      "208142510101249240089202413401192694/1668651201138451178375"
    ],
    [
      "4991467215289781887682928097964/472980963875293225",
      "841613326852952451025605341333772938900552158/325286090564549507047320875"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Obtained from curve #1093, due to Dujella–Lecacheux, via two successive rational 2-isogenies. The first quotient has torsion \\(\\mathbf Z/2\\mathbf Z\\times\\mathbf Z/4\\mathbf Z\\); quotienting by the appropriate rational 2-torsion subgroup gives a curve with torsion \\(\\mathbf Z/4\\mathbf Z\\). Its global minimal model has ainvs \\([1,0,0,-305209353709156400979315990,2052319031551796164066894280222290328100]\\) and conductor \\(3985472961137327010\\). Mapping the five independent points from #1093 through the two isogenies gives five independent points on this curve. The construction and invariants were verified in Magma.",
  "created_at": "2026-09-24 18:54:35",
  "updated_at": "2026-09-24 18:54:35"
}