{
  "id": 2956,
  "curve_key": "43961168935770766180138284805359643004161:-2186448777520530232675483274637771727448132905325076279489409",
  "ainvs": [
    "1",
    "0",
    "0",
    "-915857686161890962086214266778325895920",
    "2530612011019132213668450834761707845113339673746570387712"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 280.7523760405358,
  "faltings_height": 21.460761587040572,
  "conductor": "70656293831024198286846918376860534990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "37",
    "53",
    "59",
    "83",
    "139",
    "163",
    "1229",
    "5581",
    "22109",
    "330997"
  ],
  "discriminant": "46399369155143865505803369392250252718070351169980327577910749611801313088721940078078097565498300413108305103613952000",
  "regulator": "226383854.265109903978594051221292349289408307146774899",
  "points": [
    [
      "293748129982215501904",
      "5008036257268139104823012462608"
    ],
    [
      "93998699855862322877474464/2076481",
      "-694268526526675016423312142430703030192/2992209121"
    ],
    [
      "28087767020294462941207477504/499477801",
      "-4007086111116240394514291254830058312370608/11162829374549"
    ],
    [
      "118286889942932031314848852/159201",
      "1285421960971572207167704616237514171892/63521199"
    ],
    [
      "4875742252337175768784881001/14684224",
      "339050860586785415687681283040009245158689/56269946368"
    ],
    [
      "-193708742141956797841248863678336/8514659804121",
      "2675017216595180300023551398954629102822844261072/24845683647167232669"
    ],
    [
      "398694355130542037583836224/9247681",
      "-5843751973411416937146463842092411716432/28122197921"
    ],
    [
      "88210092206458947251654437365856/91471768249",
      "-828064310165505196244252513530045178053234963664/27664996004532307"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-093, rational kernel x=-1393367962100335136. 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 20:30:02",
  "updated_at": "2026-09-26 20:30:02"
}