{
  "id": 3222,
  "curve_key": "600942788742896158346950320683963281:-429070799755834550469165655594237881885796905989467321",
  "ainvs": [
    "1",
    "0",
    "0",
    "-12519641432143669965561465014249235",
    "496609721939623321258971611666543569867328038152225"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 247.15142341610428,
  "faltings_height": 18.557960192405265,
  "conductor": "6098008034408866436674675605910737655832159836307310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "29",
    "31",
    "53",
    "67",
    "97",
    "131",
    "191",
    "223",
    "227",
    "313",
    "433",
    "2609",
    "3881",
    "8689"
  ],
  "discriminant": "19049804055740422636703369496928562404173465091538516065578054962756653138580094345142385291506483200000",
  "regulator": "3090058055940796.3253886660477428457400076243443319492820062357139849",
  "points": [
    [
      "3876599804806421550/49",
      "392442974506308727738336095/343"
    ],
    [
      "714050068010105970",
      "596345437865988815579260065"
    ],
    [
      "3248403062355795311070/34969",
      "-76039752690198980701225646312085/6539203"
    ],
    [
      "80651201213571870",
      "-3389795941246542410660535"
    ],
    [
      "78374809310721818110/9",
      "693791631302845413226223174915/27"
    ],
    [
      "87407024296498830",
      "-8372199681770399293527495"
    ],
    [
      "39911201720738190",
      "7778849576579266716434745"
    ],
    [
      "24190783127733767538510/134689",
      "3142531100560448854102657964259735/49430863"
    ],
    [
      "159251310117558838198309230/1538443729",
      "-1062146199374335409558136667265313123345/60342378382567"
    ],
    [
      "462003408252321052942841978430/5737074057961",
      "-44829337602352787106906899941411898267739405/13741548788035288459"
    ],
    [
      "24593180254728234018000603086436030/1339423832347031209",
      "25609423577189935787902220257145516983002293532998445/1550161809106313397820679573"
    ],
    [
      "-371681472883039542422762826723090/6841781647093969",
      "18042201966096829006317416882718337813321163267055/565918399971621412755047"
    ],
    [
      "517391138415798245574787882263468030/3347926558329084169",
      "-290746472473820319855726098992532914726025760915268995/6125815096800753751159140197"
    ],
    [
      "935098301013470434070417127870/10869543016201",
      "-268790568963469755246935325459383283425031165/35835785500570060699"
    ],
    [
      "2575237184777831609055615390/19491789769",
      "-92232810223904040199195781282788119619395/2721307245019397"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-050, rational kernel x=-393203196144086129/4. 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 20:43:21",
  "updated_at": "2026-09-26 20:43:21"
}