{
  "id": 3212,
  "curve_key": "77462532905406926069830485791872801:-22714220458302941690363008707211190991182437180032049",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1613802768862644293121468453997350",
    "26289607011924700896029177487385187368561005199332"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 241.10966184590444,
  "faltings_height": 18.032056663012163,
  "conductor": "31049725562981000812793039146883386111013163212447670",
  "bad_primes": [
    "2",
    "3",
    "5",
    "31",
    "43",
    "53",
    "67",
    "83",
    "97",
    "113",
    "227",
    "271",
    "397",
    "449",
    "569",
    "881",
    "929",
    "2909",
    "4877",
    "29347"
  ],
  "discriminant": "-29586932819498736480743492690842521357191417462665474052399181216753024498921118032854290329600000000",
  "regulator": "15641852200862617.995471302700793414999128626716564384691874167012906",
  "points": [
    [
      "15453402734939004",
      "2245273645004442407027898"
    ],
    [
      "1720848148022084796/49",
      "1233322841847477584225468214/343"
    ],
    [
      "432231907918688748",
      "282984502929354572201438346"
    ],
    [
      "519899984009836556/25",
      "164063922568029433066692706/125"
    ],
    [
      "697377761407753511361/16384",
      "12356265034494147623890694426721/2097152"
    ],
    [
      "2137580594840195484/121",
      "2415512461911337387368261438/1331"
    ],
    [
      "2022545054740654098396/413449",
      "1143829169598773980778724557350686/265847707"
    ],
    [
      "-130499690913801610164/2809",
      "-148330119940849268221723230654/148877"
    ],
    [
      "-446556582555143887716/19321",
      "-19224645113439615764187068710338/2685619"
    ],
    [
      "563579324167136685725480586396/21915440420449",
      "-137469464210196932390476074726869599722689814/102594789376207005457"
    ],
    [
      "393671470259812850147335159724/5404504408081",
      "-215878771248534826385650234037232468268403258/12564170263225977479"
    ],
    [
      "420573481298932770774732111084/24394817470321",
      "-228340464638856226372266155110406379050969562/120488711310654624631"
    ],
    [
      "55936880181194701864655921943836174124/1745941936607226541681",
      "-199414740524496347897328366200363175170962146637616629542/72953258543490178614969782278921"
    ],
    [
      "-4302865350045018513213664/179479609",
      "-17205081039690217633856102263970666846/2404488321773"
    ],
    [
      "2450244716637695959762185060355625753766/9283565747381508863809",
      "-119961553841626692118723150715856525998119669647620224409964/894483278433101995948780462692127"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-049, rational kernel x=373285797610436767/4. 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 20:42:55",
  "updated_at": "2026-09-26 20:42:55"
}