{
  "id": 3017,
  "curve_key": "-51460858304:-138046371262415360",
  "ainvs": [
    "0",
    "-1",
    "0",
    "1072101215",
    "159775535297761"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "naive_height": 78.93273209453056,
  "faltings_height": 4.636598088273737,
  "conductor": "77883686473803072",
  "bad_primes": [
    "2",
    "3",
    "17",
    "47",
    "89",
    "257",
    "457",
    "2857"
  ],
  "discriminant": "-11107106649118160852288642777088",
  "regulator": "35440.6385547988360079809244718875222981502188270457983",
  "points": [
    [
      "28463",
      "14606472"
    ],
    [
      "93663",
      "-32891728"
    ],
    [
      "169443",
      "72154508"
    ],
    [
      "7416111",
      "20196151544"
    ],
    [
      "21991465/256",
      "-121906620501/4096"
    ],
    [
      "49425",
      "-18261944"
    ],
    [
      "3813417/16",
      "-7560165965/64"
    ],
    [
      "8597569",
      "-25209642312"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1352 via the rational 2-torsion point x=23857. 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 20:33:29",
  "updated_at": "2026-09-26 20:33:29"
}