{
  "id": 2724,
  "curve_key": "699735892560936761575271815910679830570173914721:-3432362064940977532699069342819984618934073651759274051701448872977322769",
  "ainvs": [
    "1",
    "0",
    "0",
    "-14577831095019515866151496164805829803545289890",
    "3972641278866872144327625339370539094362188991726331233427897011245892"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 334.0387507368206,
  "faltings_height": 25.893868018012025,
  "conductor": "8802038786118636750817053683370",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23",
    "29",
    "163",
    "239",
    "373",
    "881",
    "160591",
    "146251529"
  ],
  "discriminant": "-6619500831203115609617277340713252154956149208246653933036305165820042962327143869067935597280022464547570834532882118785504787824640000000000",
  "regulator": "11876721.82441189459042287089219066343983826608",
  "points": [
    [
      "16399897335548784918633584881066404096105451663369/2256331984482434191675456",
      "66405494185231859547269394364979695712749254309319171310698566700339237073/3389256983895918481537893117007248896"
    ],
    [
      "416309849925662980820155460688674632766256042912769261879004403672538136164/23228548709235437608973721548070279585371821836961",
      "8494059997256953732670839956975876985088584271961473372173611947955299331732705346963651193996863595696223759442/111952324321780282914319255060454964476975322608017115301511362848265314959"
    ],
    [
      "-114296281541622663062818562867160716/2667476164081",
      "-292855287907170618614227992270993742380132657788434882/4356631437699816521"
    ],
    [
      "-208165126777807650411964955941779356/2434445593441",
      "-257450455653443029799839564787424404943664385008238702/3798394860523782511"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z10-021, rational kernel x=1509973410712173067946207/4. 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 20:19:28",
  "updated_at": "2026-09-26 20:19:28"
}