{
  "id": 3136,
  "curve_key": "806750434544453507575635571951834559320228225:-22883399297202479384706612336264237168915937871327195174014915074625",
  "ainvs": [
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    "0",
    "0",
    "-16807300719676114741159074415663219985838088",
    "26485415853243610398964585891912523713720572243019985442333257792"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    4
  ],
  "naive_height": 310.204764825953,
  "faltings_height": 23.635005639496754,
  "conductor": "16491334853285711166878253103438065925189351213350",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "29",
    "31",
    "41",
    "73",
    "79",
    "83",
    "241",
    "281",
    "5417",
    "488399",
    "41465951",
    "58252159873"
  ],
  "discriminant": "822073273213488967035119739800754333198182281635839850752411690516194178448384474177543938046642789851281897504426422435840000000",
  "regulator": "251537253420.431384735224928248833665684429377710258906982308",
  "points": [
    [
      "103537673170890124687875300692/35366809",
      "10243145676995880519073995435048263319016856/210326413123"
    ],
    [
      "53669882994240811524368",
      "-12398314172672731340761475016688648"
    ],
    [
      "2769370223832300118172",
      "-34339734481312360650343220646136"
    ],
    [
      "5618288406133155590672",
      "-330755727803203965189275759414536"
    ],
    [
      "406369413634260878673752381456/13432225",
      "256784252226667786908852069746410527872217976/49229104625"
    ],
    [
      "824222640856707743194832/361",
      "25065133723600799553259678479288296/6859"
    ],
    [
      "10368123201368124263470352/5041",
      "8893698072959163454389196802507871304/357911"
    ],
    [
      "118991967919531870238864/25",
      "-29132349739590412368537301031996648/125"
    ],
    [
      "-1448461224197917863539989575054064/1165387179961",
      "268223674683005242216723605257284172887175947659880/1258071587770478291"
    ],
    [
      "1335045743559744192272",
      "80164927031290377516102577372664"
    ],
    [
      "2266893509302689197072",
      "5846479591535370715129069756664"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2z2old1011121314-045, rational kernel x=-19501586197533110816897/4. Source: https://dujella.github.io/tors/z2z2old1011121314.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 20:38:58",
  "updated_at": "2026-09-26 20:38:58"
}