{
  "id": 2710,
  "curve_key": "190617977329921:-2406970854305220149281",
  "ainvs": [
    "1",
    "0",
    "0",
    "-3971207861040",
    "2785845565252608975"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4,
    2
  ],
  "naive_height": 98.64387726712538,
  "faltings_height": 6.186252471871657,
  "conductor": "880838805",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "31",
    "73",
    "337"
  ],
  "discriminant": "655460745409415551307230784688150650625",
  "regulator": "52.630404042721543665703172092498421407385587",
  "points": [
    [
      "51721719495/61009",
      "2536493818599330/15069223"
    ],
    [
      "46529430",
      "-317125234515"
    ],
    [
      "6248998905/256",
      "-492435738133365/4096"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1570 via the rational 2-torsion point x=18231631/4. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:18:46",
  "updated_at": "2026-09-26 20:18:46"
}