{
  "id": 3184,
  "curve_key": "472821722418623027967660921696:-324639560011262631252761826712862149979631744",
  "ainvs": [
    "0",
    "0",
    "0",
    "-9850452550387979749326269202",
    "375740231494516934320326188325071932846796"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 204.98554776023263,
  "faltings_height": 14.870165417147264,
  "conductor": "2283940066993910894016063059625994348127085137280",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "23",
    "47",
    "53",
    "59",
    "97",
    "107",
    "139",
    "181",
    "191",
    "197",
    "727",
    "757",
    "761",
    "809",
    "839"
  ],
  "discriminant": "181342925315636466845645352743120757502743207149636907713607069167755482980139360000",
  "regulator": "4753988404611.14882092927599706315018965991346389283976023003482126",
  "points": [
    [
      "59597179662347",
      "-18966381943719671125"
    ],
    [
      "468341603149027",
      "-9924223759723946107305"
    ],
    [
      "1490506586694163/9",
      "48948784237354600817855/27"
    ],
    [
      "3927182152411313/64",
      "-24783741853059930038935/512"
    ],
    [
      "99675418637947",
      "-619827702367609645875"
    ],
    [
      "404209324877147",
      "-7901639581699037769725"
    ],
    [
      "16588293396294427/121",
      "-1684606892467524851016765/1331"
    ],
    [
      "49698419359167682/841",
      "-6322754171901949907580/24389"
    ],
    [
      "-111608524232053",
      "291354228825450335125"
    ],
    [
      "99482034251895654833210/1681246009",
      "-484696087328740972706844703318208/68936130107027"
    ],
    [
      "1017897015741497/16",
      "-5180987955984980058605/64"
    ],
    [
      "-14098873308549741854/143641",
      "34300367419186338970177363140/54439939"
    ],
    [
      "116165627047871378/5329",
      "161041286870798098866100220/389017"
    ],
    [
      "128707878782441962/1521",
      "-22830246417322869214639600/59319"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-053, rational kernel x=-118188654139412. Source: https://dujella.github.io/tors/z2old141516171819.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 20:41:29",
  "updated_at": "2026-09-26 20:41:29"
}