{
  "id": 2888,
  "curve_key": "117442109848221623562494881:-2800505521940514585978493077804013140721",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2446710621837950490885310",
    "3241325835579095396775139751584108100"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 181.6612371424062,
  "faltings_height": 13.186586700027087,
  "conductor": "1181838693760983713230230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "31",
    "41",
    "47",
    "61",
    "71",
    "157",
    "1039",
    "10257671"
  ],
  "discriminant": "-3601269305564080125392954307880944095127910098257218454783357376000000000000",
  "regulator": "354542.8912654179008853453424240555888648594512467304",
  "points": [
    [
      "2057938690220",
      "2630920009494099890"
    ],
    [
      "1128694977782639680/1026169",
      "1425620760799407400291095830/1039509197"
    ],
    [
      "-1825530227680",
      "1274434081288494290"
    ],
    [
      "44591928273970",
      "-297594569683082696360"
    ],
    [
      "-185989622606020/121",
      "-2443562290197981770570/1331"
    ],
    [
      "2082444617720",
      "-2678968185132140110"
    ],
    [
      "-6340420838098691581256740/3854817830161",
      "-12700223906241336521440652080058993950/7568429828385372409"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-127, rational kernel x=16111853758239/4. Source: https://dujella.github.io/tors/z6old678.html. Independent witness points transported by 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 20:26:59",
  "updated_at": "2026-09-26 20:26:59"
}