{
  "id": 2734,
  "curve_key": "86936476903085278566941008162140798026462161:-778021968640662652167905778719283910691387573667131073217243746841",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1811176602147609970144604336711266625551295",
    "900488389630396588157147423615658892099001345086675766227088025"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 303.52125482152655,
  "faltings_height": 23.222330481137266,
  "conductor": "10344178476746183675100326370",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "23",
    "47",
    "59",
    "61",
    "89",
    "139",
    "2069",
    "5981",
    "442271"
  ],
  "discriminant": "29944126318009522061008632142418316298700269399955227192873406083045720967701903218221141650973953316540992640955367490294400000",
  "regulator": "5697446.096509431835613684344855346540935672590",
  "points": [
    [
      "197079459824218474722104566638454/117796536225",
      "-2042922399233834272359628659624888050127522266797/40429538180463375"
    ],
    [
      "421505620680076677867465954570372074843692/668611550978914316761",
      "-52536706290993329172076951736938507871285568836728355208704581/17288639272248697457136247620509"
    ],
    [
      "156534098061080284105664952573322380399271217920/982611306736401655700343889",
      "-764476441682524175190203904918915584701382124282281877067136379209921405/30801554545322255785819642080688666346713"
    ],
    [
      "11006288954559141477268668850766889242085010339785664246134646690/8423607433116667161279432336307739839241209",
      "-676044497705043072003296505972075667138707142703212040793841984264147570558375589816339555833055/24448216270997245951441497823188132131501073247272540359579921677"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z10-016, rational kernel x=773507848541288941990. 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 20:19:55",
  "updated_at": "2026-09-26 20:19:55"
}