{
  "id": 2977,
  "curve_key": "63245381387069306964414951540837555049:-528337644765232755806998993322790181840185018368811564853",
  "ainvs": [
    "1",
    "0",
    "1",
    "-1317612112230610561758644823767449064",
    "611501903663463837629781158845122941427734480390688926"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 261.2186611594547,
  "faltings_height": 19.705055474402222,
  "conductor": "220983838255926673069783016840911590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "23",
    "29",
    "37",
    "41",
    "43",
    "61",
    "103",
    "109",
    "211",
    "229",
    "499",
    "1429",
    "2640739"
  ],
  "discriminant": "-15139187414688141317262058211046790009890999899030865378231096782323429585890388166502847359599242093877917320",
  "regulator": "3164174725.51702508233442425771810483567797408976789312",
  "points": [
    [
      "-135953973075499104",
      "-887763257997686062398308294"
    ],
    [
      "1312428102955619591424/1369",
      "24261673341929139546327450032593/50653"
    ],
    [
      "1002748957998087786",
      "546385665632257037405820511"
    ],
    [
      "2066335180868968446",
      "2590673627118633788956267747"
    ],
    [
      "610922047890120276",
      "-185890969407468387448161134"
    ],
    [
      "7123288212271540966/9",
      "6854570113185352709625453241/27"
    ],
    [
      "30534920265309889337091519/54081316",
      "86728430328640305532629903178888443733/397713997864"
    ],
    [
      "-106023881338787565843970/208849",
      "-102332980393027094218097439004952274/95443993"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-010, rational kernel x=666411001163892393. 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 20:31:32",
  "updated_at": "2026-09-26 20:31:32"
}