{
  "id": 3002,
  "curve_key": "24964835140588587737643646057882576:-3435020583493227020056913421105306813557183243765824",
  "ainvs": [
    "0",
    "1",
    "0",
    "-520100732095595577867575959539220",
    "3975718267931975544291553909228912485758457056100"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 237.60832892733825,
  "faltings_height": 17.78739357779257,
  "conductor": "104277816820885318880966408571860",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "29",
    "47",
    "53",
    "67",
    "79",
    "131",
    "811",
    "2659",
    "7541",
    "14633"
  ],
  "discriminant": "2175805658939839376625116874525631322365156442238175617012374480909681981677035361498629526796000000",
  "regulator": "489541700.017622535946236745813708784059983191784729167",
  "points": [
    [
      "-38570270536592082054440/1661521",
      "4029433256525839696924818371650850/2141700569"
    ],
    [
      "-158166274038084468079016/24117921",
      "315701704678428541499868946596416210/118443110031"
    ],
    [
      "-9770694417296069492315/376996",
      "49970257579624036060680880580975/231475544"
    ],
    [
      "2947184641357387839013936/390181009",
      "-5329423117836516821446742537938454090/7707245470777"
    ],
    [
      "9543403483341410694195/546121",
      "-190734391984281169408265332741290/403583419"
    ],
    [
      "18623783253712540",
      "-865474842494318711424770"
    ],
    [
      "-4911556896576238227485598920/189520044921",
      "-18226565120166934993088752507352280940630/82505466835863219"
    ],
    [
      "116142359850766880",
      "-38861546931445499922172330"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-068, rational kernel x=12974179118756332. 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 20:32:51",
  "updated_at": "2026-09-26 20:32:51"
}