{
  "id": 3005,
  "curve_key": "10575004227593224476398652095485489:-1087475549058673248391479297350877089817130113562537",
  "ainvs": [
    "1",
    "0",
    "0",
    "-220312588074858843258305251989281",
    "1258652255854945870982607587917870804651796261961"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 235.03140358052454,
  "faltings_height": 17.18275973119395,
  "conductor": "3075048733534976572545414248070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "19",
    "23",
    "37",
    "61",
    "67",
    "307",
    "647",
    "13709",
    "29303",
    "87961"
  ],
  "discriminant": "4171237431583574120627698643374640684163080048441804917054624376590778471687868766517565849600",
  "regulator": "9238963.51183484265268656985809241029296499779900671033",
  "points": [
    [
      "165399424187200545665386/19228225",
      "405093807999023999392023739198379/84315766625"
    ],
    [
      "6854977819654343069950/434281",
      "374673062558878804677820948985249/286191179"
    ],
    [
      "9572394980638078",
      "-163886653036920132550493"
    ],
    [
      "8556322849230706",
      "820662434832307957147"
    ],
    [
      "212794650498411176142166218154/49077772835809",
      "213310498099684178122088552924025196758753019/343816938723220247377"
    ],
    [
      "8181826374515434",
      "61668847653574622544523"
    ],
    [
      "3098249738425562641792/237169",
      "-90205080975914030240127854568965/115501303"
    ],
    [
      "2157649605503378554/169",
      "-1594812232056911245075000601/2197"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-114, rational kernel x=-68458819008845649/4. 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 20:32:58",
  "updated_at": "2026-09-26 20:32:58"
}