{
  "id": 3218,
  "curve_key": "34887326047193403357090493936561:-324466305723179177263433598599433783977039559145",
  "ainvs": [
    "1",
    "0",
    "0",
    "-726819292649862569939385290345",
    "375539705698123987190329314594130495765391961"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 218.79702176208366,
  "faltings_height": 16.2663465962614,
  "conductor": "23989560829689213420672070983398343053293012701577866",
  "bad_primes": [
    "2",
    "3",
    "7",
    "71",
    "79",
    "89",
    "103",
    "257",
    "821",
    "1327",
    "1579",
    "2543",
    "2719",
    "4831",
    "8369",
    "15511",
    "395849"
  ],
  "discriminant": "-36351926352773507551734212592902302889800277268922166282069900832990856517581807029476917248",
  "regulator": "46098410676444245.459706886971035453216394189145722584287405840988474",
  "points": [
    [
      "340993186755166",
      "12936333282110130727291"
    ],
    [
      "568969835333086",
      "12090994900661403086971"
    ],
    [
      "-25528055317834646/25",
      "-909983836032576135299977/125"
    ],
    [
      "203753315272042378/361",
      "82625797267972502329020001/6859"
    ],
    [
      "1916212243211842522/49",
      "2651939140060244947288050949/343"
    ],
    [
      "12501548857791549706/3721",
      "42981282428133259818912129583/226981"
    ],
    [
      "3795011245420226878/14161",
      "23832098742442348769119853117/1685159"
    ],
    [
      "-33240926223581230044046214/82282348801",
      "-579698603328790360025992007568841169021/23602609471218049"
    ],
    [
      "366384312483871185022/452929",
      "5426517925901910668775800114011/304821217"
    ],
    [
      "151722099166111896432338650364024717884906/274277967763893427427823961",
      "-54272454714773765227847570155380617055992830111964694897479063/4542410555830416092113555251209298919459"
    ],
    [
      "102580991259600251797654299068813938234/8051669891037163577761",
      "-1036729416034911302254766799365925580176920696902967724589/722485177487822351397247730272241"
    ],
    [
      "176545340569128577392842730556410/133001422610347201",
      "-2028868528325177685434119764744733739136774277149/48504767749890340592960801"
    ],
    [
      "-362673372359872285842822632/1442523504601",
      "-40349377693173512257148741039608194889151/1732544297724535651"
    ],
    [
      "-45329188976457388432207872293272358/648721213331977834801",
      "-341023420721433658100682463442073589964440733664501371/16522933293849658657377131860951"
    ],
    [
      "177916833418159953360212124634/18466142700625",
      "-74767102954979831113879863662775478895829173/79353170066693265625"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-048, rational kernel x=8340799720431663/4. 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 20:43:10",
  "updated_at": "2026-09-26 20:43:10"
}