{
  "id": 2742,
  "curve_key": "57636583154761841264791106493778450890145:-13792021719528356250642771262036385537166228591182567196029425",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1200762149057538359683148051953717726878",
    "15962988101305967882588329151972503212116946679909605925572"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 281.56492835123464,
  "faltings_height": 21.282294325601235,
  "conductor": "270662653535270356603978350",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "29",
    "31",
    "47",
    "61",
    "71",
    "157",
    "241",
    "307",
    "580219"
  ],
  "discriminant": "721913531590592966763893000216812275944212979119045583069110613121160468844364945930425014999301325028865873187456000",
  "regulator": "6373674.334975949761686474489569252093857518357",
  "points": [
    [
      "-4114999072350270948636522131207988/119401361430649",
      "-167144582648038980364604225786336644517185663140630/1304709780679314673357"
    ],
    [
      "944955350155606487363352105480043858550976/411161442969917505121",
      "918476074967289465049234859168463344862577035308735671821665106/8337168372095986631579394759919"
    ],
    [
      "1913528408618805072532913250731424/66449642272225",
      "39302721571038954589953282058212877149036468946638/541675223173017004625"
    ],
    [
      "1424464915402967511202906955000884541519645910943518/77765172736848738105605164000129",
      "-7325524991928213910643955858455377582597993712063568528567232812201942776148/685768782829219185855215745505745540446464781633"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z10-008, rational kernel x=319985493971327392543/4. Source: https://dujella.github.io/tors/z10.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 20:20:17",
  "updated_at": "2026-09-26 20:20:17"
}