{
  "id": 3132,
  "curve_key": "170343311257867386908942395619082166681:1259993900031946568467263168971470838260168752801137408579",
  "ainvs": [
    "1",
    "0",
    "1",
    "-3548818984538903893936299908730878473",
    "-1458326273185123343429141360947073979888405493321482244"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 264.09263767925665,
  "faltings_height": 20.052777906795654,
  "conductor": "233675553798276919489685212875169920733360530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "29",
    "31",
    "41",
    "43",
    "59",
    "79",
    "173",
    "223",
    "257",
    "347",
    "599",
    "1801",
    "5347",
    "129581",
    "149803"
  ],
  "discriminant": "1941690166862869654225798673188381676791619807992217911851987485964956457376782707237134977419666950731506250000",
  "regulator": "32894739751.4404415023167691765487766024757032072650091077704",
  "points": [
    [
      "17222907174954573290755/3969",
      "-2013650810646262819432925072389406/250047"
    ],
    [
      "41290823063588027319780280051495/19998703504081",
      "-11306776247112790313602474641329165658504826358/89434022081918695271"
    ],
    [
      "6675779752997360380",
      "-16503441341439942292765123933"
    ],
    [
      "-34581595466257140958078921145/79646435089",
      "-585345554763935988405288803596423911961774/22477577971512313"
    ],
    [
      "68070121438421139150926543153980/15949344157569",
      "-498034529030025734978978869048068886189941592931/63696305636349485247"
    ],
    [
      "373003649726212886327702050299895/91744865349316",
      "-6295121098217837162529990482694096348841219446947/878764797998082305864"
    ],
    [
      "38240704903715296033870/17161",
      "-2929967326986743473771782924055343/2248091"
    ],
    [
      "75602957101954478780450677763324282015326454983/21110186219413840566332849689",
      "-17287189288982198565746954579775706660194818789517881699599739580955622/3067171757375431840758442033485297627680387"
    ],
    [
      "7836607467450425933761305216880/186091292689",
      "-21915577129323475587403440964833827027651806651/80276620114058887"
    ],
    [
      "41624597374521703108125553251210281289640124539/127894142864039454148155625",
      "-8492152492766499823963438277395212061383936333193750660655802078381062/1446358604174159220917225878004903796875"
    ],
    [
      "122649416216339362983218821260085946013282400439008255/13366954299224166477009159397277689",
      "-41996987855376008949337293121525768257644352716104291168575156555630947348284526/1545427709392070299423927193869583988990685170566387"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-010, rational kernel x=13031852518377921639/4. Source: https://dujella.github.io/tors/z4old9101112.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 20:38:46",
  "updated_at": "2026-09-26 20:38:46"
}