{
  "id": 2727,
  "curve_key": "-46801693258381267598802953874338030469526661279:-260736518573214046539464795691249303792830390115570138349936621801697425",
  "ainvs": [
    "1",
    "0",
    "0",
    "975035276216276408308394872382042301448472110",
    "301778377978256998309565817006700452968439569814815914186322136680196"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 328.8837636132675,
  "faltings_height": 25.464992724046958,
  "conductor": "10350901625769093734552060155302",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "29",
    "37",
    "71",
    "79",
    "127",
    "149",
    "1069",
    "7001",
    "9439",
    "12601"
  ],
  "discriminant": "-39401647266209058723815804751982997086428481283857346578128763306248533191747309216486109598949790555384028064778862611485089621683294911488",
  "regulator": "5571803.737943839901793189790143413037260136031",
  "points": [
    [
      "-1356967137581326215973390036919974281048/202973418074158369",
      "1570511307579493912116583053433358193395241474767765539278618/91444743897907286068642097"
    ],
    [
      "3760479806674991392656428855791540/61678219201",
      "-371395243864773365604396200226153122786882856956206/15317847416787551"
    ],
    [
      "-7702589112135690405202388/289",
      "-78739667894426492600037532945467034378/4913"
    ],
    [
      "223571536129444351984649172976220679629550252628675932166821648768664449073224246727165641886718548/45851530559281560644273206898280492031378618866337173997233492814961041",
      "3342910629813336652090975855082954324628693287375318517253743473940210155082815919575638489580531051124883238125879107914691166964191690675757594398/9818174712017894657037452554544713458984231284184349042280184863698837024659905486361263144117661868703161"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z10-020, rational kernel x=497910965560885818914783/4. 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 20:19:36",
  "updated_at": "2026-09-26 20:19:36"
}