{
  "id": 2994,
  "curve_key": "4458524224731502919734794509271421776:-9567464530844536034035115866648922821883399776885065024",
  "ainvs": [
    "0",
    "0",
    "0",
    "-92885921348572977494474885609821287",
    "11073454318107101891244347067880697710513194186209566"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 253.19592650547006,
  "faltings_height": 18.98543216124536,
  "conductor": "1983849109508312439665107289994540",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "47",
    "83",
    "97",
    "103",
    "127",
    "307",
    "10333",
    "94388321"
  ],
  "discriminant": "-1682800350522981713867877293265382978405815698001043249285206397817147687986571564214790330266643801248000",
  "regulator": "320212426.367160890996217503649355500577904420251979357",
  "points": [
    [
      "-10370628239950029",
      "109706993016836356703511950"
    ],
    [
      "95989558252153515",
      "55152725208899482417559306"
    ],
    [
      "-246659864769360093",
      "137759313149344684718350430"
    ],
    [
      "29626406927519858133243/146689",
      "1319911513211841445985081132240870/56181887"
    ],
    [
      "18801534939676913906639313327443627/17469458995870561",
      "-2484424899604889031649327944923832078873263709053430/2308974749428382454007441"
    ],
    [
      "7777619172105062883/49",
      "6221091740689884108397039330/343"
    ],
    [
      "133780549011938434383363/779689",
      "9423232677077201783081107441945330/688465387"
    ],
    [
      "18865350498723186137/16",
      "-79441595761507746065665432605/64"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-091, rational kernel x=176277529846152827. 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 20:32:25",
  "updated_at": "2026-09-26 20:32:25"
}