{
  "id": 3015,
  "curve_key": "924887262092349396290857434198889:-28128509509990060330923722961227765273617465262773",
  "ainvs": [
    "1",
    "0",
    "1",
    "-19268484626923945756059529879144",
    "32556145266192197851380590072573693098763094866"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 227.721736198063,
  "faltings_height": 16.637201153010718,
  "conductor": "1537557927687420856077617546790",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "29",
    "41",
    "43",
    "59",
    "61",
    "73",
    "83",
    "107",
    "127",
    "977",
    "182057"
  ],
  "discriminant": "-28513369178462474352150321685562836712122700206799609101906756059560127391752936436535750220",
  "regulator": "111570165.889800783019938610386276437656687139321598360",
  "points": [
    [
      "259057134963548410/121",
      "44475819732405952816793782/1331"
    ],
    [
      "2598202547437216",
      "5682628374000453876686"
    ],
    [
      "22819300985144236/9",
      "27318291706558021311074/27"
    ],
    [
      "2840280405216016",
      "27227475895795428708161"
    ],
    [
      "201876273133321066/121",
      "94610658998391756698783017/1331"
    ],
    [
      "842912232180876619/324",
      "34847792991917189440250239/5832"
    ],
    [
      "489190992598429616059/192721",
      "-90169914895500053714264167897/84604519"
    ],
    [
      "181818553298018630648491/51509329",
      "-34127265819396741182733781106694661/369682454233"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-025, rational kernel x=2534338701081673. 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 20:33:22",
  "updated_at": "2026-09-26 20:33:22"
}