{
  "id": 2866,
  "curve_key": "38969450870934752305334704473473896679466241:-185260357865750654207101456760623518964376578691811713030596056961",
  "ainvs": [
    "1",
    "0",
    "0",
    "-811863559811140673027806343197372847488880",
    "214421710492766960887781252991107774115646500735071183085158400"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4,
    2
  ],
  "naive_height": 301.1140558017886,
  "faltings_height": 23.110154051438325,
  "conductor": "4180423832258126825781263565690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23",
    "29",
    "41",
    "43",
    "53",
    "79",
    "113",
    "401",
    "719",
    "142159",
    "872959"
  ],
  "discriminant": "14385597968278853618666842530020695856872273721667081450685964667769378774686099824847948386205187865648095332748124102374560000",
  "regulator": "142133616.35844052834918490223716592616119332505753",
  "points": [
    [
      "17977892075943930816275997460/25090081",
      "95491870501532953854565837168073342154380/125676215729"
    ],
    [
      "-765111681145067451200",
      "-19689966332238030317089874965280"
    ],
    [
      "4188113713560922499261620/961",
      "8397078152303966276537538645222593620/29791"
    ],
    [
      "979983780691929317216953106140/2879809",
      "-970123021357329224681252344991792635586380540/4887035873"
    ],
    [
      "-31473760613982336671357597217560/68409971809",
      "-396299532086048920003681011301782999148168017560/17892833356559377"
    ],
    [
      "510463383456000088131888016339710146685521571875089800/702634512788124084103400091288841",
      "-52845280788925252811081715697313731350633463502226628375764069776420162827160280/18624911475355214357238338496065013995909147052389"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1119 via the rational 2-torsion point x=505910156890389864160. Independent witness points are the images of that curve's witnesses under 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 20:26:00",
  "updated_at": "2026-09-26 20:26:00"
}