{
  "id": 2735,
  "curve_key": "36308363979561748048397183763694028982823083361:-6918469340504173814990753994503978994774007627616600171434183893002641",
  "ainvs": [
    "1",
    "0",
    "0",
    "-756424249574203084341607995076958937142147570",
    "8007487662620571545128124458284733393694369249815919711100358400900"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 321.62513193636613,
  "faltings_height": 24.031468245460264,
  "conductor": "38426795181551951735578893330",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "23",
    "29",
    "31",
    "167",
    "1901",
    "2731",
    "5059",
    "8849",
    "17539"
  ],
  "discriminant": "113394414868097028545430104232888471019043402517946342102171991417040243069502924545107174957564941536406657016310000000000",
  "regulator": "22604962.97691027870480936985998159543062322482",
  "points": [
    [
      "120405351046846516442350733716/7177041",
      "3801695439501119667737511212636573382099058/19227292839"
    ],
    [
      "1082751591551438153893561693526570501540/68182385884940041",
      "-4907859094580375363293923134948553622996695098540720470/17803618987260228986560411"
    ],
    [
      "1983402805614314202111095830784385831442697607248029642640/806439917605326623729390129373241",
      "88326159131948746305294535180291134767341247307389308912932225028035187396350382913030/22901188680393683605372341483660123693422947892461"
    ],
    [
      "1252129434600921299137047473681299156972730441144363433999848532262293559390/78855796411026467657519370410127601859112470712578169",
      "1147106832272269461872509720458516441812756602107963136629289017116616742466980966887831278535976500592509770/22143712460718370738721438819924346666159423214312717284443374518215090570773197"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z10-015, rational kernel x=-7939480428474519917692. Source: https://dujella.github.io/tors/z10.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 20:19:58",
  "updated_at": "2026-09-26 20:19:58"
}