{
  "id": 4672,
  "curve_key": "-2040025991:-1050316565025293",
  "ainvs": [
    "1",
    "1",
    "0",
    "42500542",
    "1215661881042"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 69.17573600828254,
  "faltings_height": 3.8235892378122758,
  "conductor": "131859174638950710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "41",
    "43",
    "73",
    "10369",
    "470521"
  ],
  "discriminant": "-643318793555035655469446790",
  "regulator": "4584366.40874571041846578176073116608525390236799897864",
  "points": [
    [
      "-9297",
      "135276"
    ],
    [
      "67099",
      "17464200"
    ],
    [
      "-8891",
      "-363054"
    ],
    [
      "48969",
      "10963041"
    ],
    [
      "12699",
      "-1956600"
    ],
    [
      "-8483",
      "-490503"
    ],
    [
      "6147",
      "-1310448"
    ],
    [
      "270979/25",
      "-215369943/125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "I obtained this curve as a rational 2-isogenous partner of curve #4650: https://elliptic-rank.icarm.cloud/curve/4650. The source curve appears in Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. I transported eight supplied independent rational points through the isogeny and checked them exactly on this minimal model. Same rank and conductor; rational torsion Z/2Z. Source-attributed isogeny construction.",
  "created_at": "2026-10-20 20:20:02",
  "updated_at": "2026-10-20 20:20:02"
}