{
  "id": 2979,
  "curve_key": "132515707239621397067014537341465619846096:-48239303269149557729578590953935186762849976351753561503905856",
  "ainvs": [
    "0",
    "1",
    "0",
    "-2760743900825445772229469527947200413460",
    "55832526931886062186092010081594280532925797601510147899108"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 284.0625594311185,
  "faltings_height": 21.159693945914455,
  "conductor": "7055360786364598402324518744235380",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "23",
    "37",
    "61",
    "79",
    "109",
    "127",
    "1327",
    "4561",
    "56737",
    "354463"
  ],
  "discriminant": "71677001542998715805813577566805591015899130827565701836832935579786564910297363713095057078990332128687500000000",
  "regulator": "99740433.3749862864686127940160681230250306794048032857",
  "points": [
    [
      "2033588105189338273329/64",
      "-7085019067904267265805245441225/512"
    ],
    [
      "40171111099753676952",
      "-98768561514561855151517469330"
    ],
    [
      "1476256891551104256829864/8649",
      "1717121694607716802499559293085853750/804357"
    ],
    [
      "483398189937930780201/16",
      "75128938537304502834280171875/64"
    ],
    [
      "5570634871800798200697504/27889",
      "-12732521462278219587042011987338556250/4657463"
    ],
    [
      "1359634272845696348277539776/22838841",
      "-34937592307889392359571035660636727798750/109146821139"
    ],
    [
      "3179796397945733135048016/292681",
      "26076288001959948673694541244376418750/158340421"
    ],
    [
      "-57048018653767358464",
      "166331188492054551188794593750"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-097, rational kernel x=-15169814843694687956. 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 20:31:36",
  "updated_at": "2026-09-26 20:31:36"
}