{
  "id": 3075,
  "curve_key": "3782563554019287455924016:-7333265336279884121103996700743704064",
  "ainvs": [
    "0",
    "0",
    "0",
    "-78803407375401821998417",
    "8487575620694310325351848033268176"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2,
    2
  ],
  "naive_height": 169.77733260154926,
  "faltings_height": 11.965597981450994,
  "conductor": "16300273795523604802511289760",
  "bad_primes": [
    "2",
    "5",
    "11",
    "19",
    "29",
    "59",
    "61",
    "67",
    "101",
    "137",
    "1031",
    "21799",
    "224149"
  ],
  "discriminant": "198688254992514938558434815141197956652364392083054211035484812840000",
  "regulator": "529601194.34034894500780973395009675181712090765888456652",
  "points": [
    [
      "1438433583657",
      "-1694515960717754460"
    ],
    [
      "-1627573450223/81",
      "-73128907881316064800/729"
    ],
    [
      "7557225083647297/16641",
      "-552993110657235100586800/2146689"
    ],
    [
      "1563134255947516033/4485924",
      "-1451454132323078947396246375/9501187032"
    ],
    [
      "2449751767018316313/293764",
      "-3832128779105024149540507125/159220088"
    ],
    [
      "810076876920318705/4656964",
      "-66054810815412967684956897/10049728312"
    ],
    [
      "1433980006512873/9409",
      "3817463789679010480860/912673"
    ],
    [
      "1035722897888536833/5579044",
      "-210927309619329556997951655/13177701928"
    ],
    [
      "8705983598325952/47961",
      "-134599784916582348384340/10503459"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#2093 via the rational 2-torsion point x=648064835168. 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 20:36:05",
  "updated_at": "2026-09-26 20:36:05"
}