{
  "id": 3173,
  "curve_key": "363527146969258974997747825:-6069787001198338624728246296190455215625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-7573482228526228645786413",
    "7025216436568995568432843580877282531"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 183.47368862464012,
  "faltings_height": 13.274230236433189,
  "conductor": "10598095089074167643269066006409167869829050",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "31",
    "61",
    "73",
    "163",
    "173",
    "193",
    "211",
    "229",
    "997",
    "1163",
    "1723",
    "2269",
    "6959",
    "21871"
  ],
  "discriminant": "6480625236772527124768545202714046000730979877954336231865644323194216000000",
  "regulator": "338468138323.7336819266498090206996937997048462460345251976100981",
  "points": [
    [
      "3394161830119",
      "-4519013963505250012"
    ],
    [
      "2281504290385",
      "1273620243340930682"
    ],
    [
      "2343530248735",
      "1465438682862181532"
    ],
    [
      "2663724915535",
      "2398293466180219532"
    ],
    [
      "3799553023235",
      "5753432586059784732"
    ],
    [
      "2541371007235",
      "2047387840747784732"
    ],
    [
      "2001932334308355/2401",
      "-133632559850568431265472/117649"
    ],
    [
      "-49513533967159357958712465/42963790574329",
      "-1062047944710391852496382461213657476764/281613769910371086733"
    ],
    [
      "5153132332915470135/4695889",
      "-1924754850355559280843986004/10175991463"
    ],
    [
      "-111530423318561/36",
      "187442886950048484817/216"
    ],
    [
      "3487691321205628960335/689640121",
      "-179348608564771933524881036740508/18110639217581"
    ],
    [
      "96150190465003111519/87422500",
      "-131910821415416478753434120303/817400375000"
    ],
    [
      "-2338857394062505/6724",
      "-1709904909677465286160929/551368"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#2164 via the rational 2-torsion point x=1566508746135. 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 20:40:48",
  "updated_at": "2026-09-26 20:40:48"
}