{
  "id": 2980,
  "curve_key": "452639219433694423950818594441318999121:-9629952668272111514254314231453915016190365296020402942169",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-9429983738201967165642054050860812482",
    "11145778551240869810522211480214745282371584457183262081"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 267.02447619258766,
  "faltings_height": 19.878902231570265,
  "conductor": "2900021013294811715348347320974526390",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23",
    "29",
    "37",
    "47",
    "61",
    "71",
    "229",
    "349",
    "823",
    "6301",
    "7669",
    "11959",
    "24107"
  ],
  "discriminant": "1018051610086532888073503415119531141046455847234621491636511730278642712888971416017105623446805180155208000",
  "regulator": "10182493315.8246430606195410057615464105171079746283083",
  "points": [
    [
      "16102815220062302425/9",
      "-975196123774865677303843651/27"
    ],
    [
      "321734126322310023502198591/180579844",
      "42046627596989307700080520876998389437/2426631943672"
    ],
    [
      "2469707791210308675",
      "-1708903060184370118904367353"
    ],
    [
      "3599702496048119496031/2025",
      "-305760556778328950493212007589/91125"
    ],
    [
      "2473318563385986605719/121",
      "121689405914299609204342401177101/1331"
    ],
    [
      "72498656982705259631427120665509/24479369161569",
      "367256930019968118239232713990527693644275415833/121115669064035963247"
    ],
    [
      "36131051051110961884341867353509/20325914014329",
      "275023277182368673515310850109522285744944677/91637899541879250483"
    ],
    [
      "23613704940358326439881283719751/14607974473444",
      "19838165499488233061338381231175040348330793673/55832233540532958872"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-020, rational kernel x=-884241588715000959. 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 20:31:39",
  "updated_at": "2026-09-26 20:31:39"
}