{
  "id": 3012,
  "curve_key": "163882723790857327580405657629249:-1769919462938324285644263074003878417848171991393",
  "ainvs": [
    "1",
    "0",
    "0",
    "-3414223412309527657925117867276",
    "2048517896919356527569649754303110008379265680"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 222.53011158901262,
  "faltings_height": 16.540492633571354,
  "conductor": "1991379159914908277187907157210",
  "bad_primes": [
    "2",
    "5",
    "11",
    "13",
    "19",
    "23",
    "31",
    "43",
    "53",
    "61",
    "73",
    "97",
    "103",
    "223",
    "271",
    "1987",
    "8443"
  ],
  "discriminant": "734301549282852131907312401457717474529939170364457462102069294774781956830985263452363161600",
  "regulator": "7033607.32397847601202648198731196589829300140211528811",
  "points": [
    [
      "2786059168719804",
      "119004330069550905194660"
    ],
    [
      "581806489926768",
      "16094761323775942519516"
    ],
    [
      "-26494341925818512908520/37442161",
      "14688241181936141211623784056521900/229108583159"
    ],
    [
      "424028777166828",
      "26019789637417966394276"
    ],
    [
      "152388600176653639992/76729",
      "-1183668701078723418740783594812/21253933"
    ],
    [
      "473654344347928",
      "23186628611991338815796"
    ],
    [
      "449432353432344",
      "24593413997572330000180"
    ],
    [
      "13022828720789726156312/2879809",
      "-1374327401098457188583615573472332/4887035873"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-060, rational kernel x=-11158741786780865/4. 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 20:33:14",
  "updated_at": "2026-09-26 20:33:14"
}