{
  "id": 2910,
  "curve_key": "250118537932496962428572161:-3939144869083574701166881937225742211841",
  "ainvs": [
    "1",
    "1",
    "1",
    "-5210802873593686717261920",
    "4559195450326040291819893761582786945"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4
  ],
  "naive_height": 182.35193156722477,
  "faltings_height": 13.024461462630777,
  "conductor": "548088118837830139058490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "29",
    "31",
    "37",
    "47",
    "59",
    "61",
    "349",
    "21269"
  ],
  "discriminant": "75447976164590962961620349524966179459183076488903823196160000000000000000",
  "regulator": "1965606.217744365299818339264942494843646289636127023",
  "points": [
    [
      "10199403067316397/6889",
      "171276056690467005708631/571787"
    ],
    [
      "536262284932253/361",
      "2131845669143276528967/6859"
    ],
    [
      "1394958071573",
      "69310365770964213"
    ],
    [
      "4598358387048557/2809",
      "96013258617980079138801/148877"
    ],
    [
      "194903562814587/169",
      "635276519251051813461/2197"
    ],
    [
      "63001708882803053/32761",
      "7617699475306313103358833/5929741"
    ],
    [
      "54038049619101077/37249",
      "1654313818251871148581941/7189057"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2z4old678-067, rational kernel x=-11094864572589/4. Source: https://dujella.github.io/tors/z2z4old678.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 20:27:59",
  "updated_at": "2026-09-26 20:27:59"
}