{
  "id": 3203,
  "curve_key": "218816392504197398920984246210710121:-59968890097741374856028774276987589726546751779583669",
  "ainvs": [
    "1",
    "0",
    "1",
    "-4558674843837445810853838462723128",
    "69408437613126590888662251760059596464201831554998"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 244.1206231697473,
  "faltings_height": 18.386498864826596,
  "conductor": "1753089367555057839284708707858690346751194714173298539554510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "23",
    "31",
    "41",
    "43",
    "137",
    "197",
    "313",
    "353",
    "457",
    "509",
    "757",
    "1447",
    "4583",
    "4969",
    "104579",
    "738547"
  ],
  "discriminant": "3981941762460561343555472172816100414236359376523536789477216738158867620176959707987757265554031450000",
  "regulator": "91118684888976897.978770343027544276679005892846577046120431950283987",
  "points": [
    [
      "15262030261855914",
      "1840864545737137709689495"
    ],
    [
      "352750779051217626/49",
      "2085362420895642710960840050/343"
    ],
    [
      "42041248770915712041/2809",
      "-316971122126852502649607838325/148877"
    ],
    [
      "210229268311262224809/121",
      "-3045891797783604097315518549835/1331"
    ],
    [
      "135511501333868309841/2209",
      "-471358648455483223716890909575/103823"
    ],
    [
      "4072331329079665291626/9409",
      "-256806120318318675537149161269065/912673"
    ],
    [
      "33329555545330414946/2209",
      "209239119844013247857468774130/103823"
    ],
    [
      "2235633811433047784073/1369",
      "105616789250808940048772104815835/50653"
    ],
    [
      "108543656047255533039740454509977053/7182085526882286241",
      "-38324443573032385943717194773663643271260673556529373/19247567831904579415263954289"
    ],
    [
      "38308491519865608234/152881",
      "493893133583701027965468803481265/59776471"
    ],
    [
      "2628353951719829616696976250957491959771239151/469755696431930883374586776164",
      "-2137542266931730473236394884660718682864379983191026455000795636077155/321964569736529517375093048686384153565108712"
    ],
    [
      "299481643084124912479032269804549/4327391116502281",
      "-2630393743104078750815380186583621282173509404565/284668376024277949315429"
    ],
    [
      "-605425138218512765863063836/10545441481",
      "-12899875112976728811538015746932714233205/1082921931125371"
    ],
    [
      "763844944653343835660376/47844889",
      "-276544508928358098236413784704397935/330943097213"
    ],
    [
      "75143158113151271433432/14161",
      "-20596769432239052962942467794972530/1685159"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-036, rational kernel x=593026323000703735/4. 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 20:42:30",
  "updated_at": "2026-09-26 20:42:30"
}