{
  "id": 3083,
  "curve_key": "1021853955129659892656246667897424081:-1032181431288525515139078235787622575552839330550584729",
  "ainvs": [
    "1",
    "0",
    "0",
    "-21288624065201247763671805581196335",
    "1194654434361719344451732989691125852509802463778297"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "naive_height": 248.7440457849256,
  "faltings_height": 18.49184765077619,
  "conductor": "43591641500121819666966659383620704342130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "31",
    "41",
    "43",
    "61",
    "83",
    "101",
    "107",
    "137",
    "439",
    "37463414931029"
  ],
  "discriminant": "929734782426074357090627058392563886539643542927166109839073953738629805708847250042797284627696040000",
  "regulator": "38681297320.91886506575822147608691202236024750277452714836",
  "points": [
    [
      "95872310786639754",
      "-5905522380130812292039947"
    ],
    [
      "95047692742948704",
      "-5466878926417961718493707"
    ],
    [
      "90381337358197824",
      "-2977572378369673139892597"
    ],
    [
      "89289009630428964",
      "-2381876776656314452564227"
    ],
    [
      "433552460185168371/4",
      "101370570555549972027098799/8"
    ],
    [
      "86722230854575638",
      "-820533908388034276043499"
    ],
    [
      "90771437150444172",
      "-3187867041122986935858297"
    ],
    [
      "86267723154447894",
      "-384785741033773546770987"
    ],
    [
      "110583347654293584",
      "13884348464504283386681883"
    ],
    [
      "331348242976734266667954/3728761",
      "-15445300149877710636750528203360517/7200237491"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-033, rational kernel x=-41172155077932666. 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 20:36:26",
  "updated_at": "2026-09-26 20:36:26"
}