{
  "id": 2906,
  "curve_key": "-2676385554812123217120464879:-1216599644717894679286549515476135584546169",
  "ainvs": [
    "1",
    "1",
    "1",
    "55758032391919233690009685",
    "1408101440645734666872928942592898134297"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4
  ],
  "naive_height": 193.8092673932513,
  "faltings_height": 14.210397082644525,
  "conductor": "23959330209511704615223770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "23",
    "31",
    "41",
    "43",
    "97",
    "193",
    "241",
    "2087",
    "2713"
  ],
  "discriminant": "-867642217212625083846002768955713227450543902249209956662139865103797360400000000",
  "regulator": "56596369.66823016230298848545642336087228040168738221",
  "points": [
    [
      "4698540183107",
      "-42116615275164168154"
    ],
    [
      "33716514285132881107/998001",
      "203963650828708484509742960954/997002999"
    ],
    [
      "-3238133643109",
      "-34548457088047029466"
    ],
    [
      "9355813250315323/4489",
      "-11777333331094773248673502/300763"
    ],
    [
      "16088796947707",
      "80434787492716063646"
    ],
    [
      "10748450432707",
      "57001517630502058646"
    ],
    [
      "-892504265425088033/128881",
      "1215262019440810506848661934/46268279"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2z4old678-054, rational kernel x=4782017598099. Source: https://dujella.github.io/tors/z2z4old678.html. Independent witness points transported by the degree-2 isogeny.",
  "created_at": "2026-09-26 20:27:48",
  "updated_at": "2026-09-26 20:27:48"
}