{
  "id": 4548,
  "curve_key": "68061553:-560926596905",
  "ainvs": [
    "1",
    "1",
    "1",
    "-1417949",
    "648629786"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 54.10776913463514,
  "faltings_height": 2.2834235817548163,
  "conductor": "204122451",
  "bad_primes": [
    "3",
    "13",
    "17",
    "37",
    "53",
    "157"
  ],
  "discriminant": "374993775020226609",
  "regulator": "3070.533170913963934944849540655107248113057435",
  "points": [
    [
      "27238",
      "-4504840"
    ],
    [
      "25342/9",
      "-3758848/27"
    ],
    [
      "73182/49",
      "-15069305/343"
    ],
    [
      "2142678/841",
      "2811270629/24389"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained as a rational 2-isogenous partner of ICARM curve #4377, submitted by Volkan Dagli. The partner has the same rank lower bound and conductor and has torsion subgroup Z/2Z × Z/2Z. Four rational witness points were transported through the degree-2 isogeny.",
  "created_at": "2026-10-17 13:16:33",
  "updated_at": "2026-10-17 13:16:33"
}