{
  "id": 4295,
  "curve_key": "256852084288:-128812888547740160",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-5351085089",
    "149090775069729"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 78.81529862589922,
  "faltings_height": 4.435065812109007,
  "conductor": "5377165292352",
  "bad_primes": [
    "2",
    "3",
    "7",
    "137",
    "193",
    "337",
    "449"
  ],
  "discriminant": "204016524837476185707106074624",
  "regulator": "693682.73777603233343908203632463241027034981100740",
  "points": [
    [
      "20136097/144",
      "-79845170185/1728"
    ],
    [
      "20721637/324",
      "-48252214675/5832"
    ],
    [
      "56081",
      "-5037120"
    ],
    [
      "185253/4",
      "-6199725/8"
    ],
    [
      "27739553/529",
      "-43322169600/12167"
    ],
    [
      "46770981/676",
      "184384901085/17576"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve#4087, submitted by jesper-petersen, whose source curve was found using a Tate-normal-form discriminant sieve. This isogenous curve has the same rank and conductor, with torsion subgroup Z/2 x Z/2. The six supplied points were transported from the source curve.",
  "created_at": "2026-10-16 19:00:23",
  "updated_at": "2026-10-16 19:00:23"
}