{
  "id": 3210,
  "curve_key": "100689992280979363656102373057754425:-21321087381918523782085579929806039186787068168918125",
  "ainvs": [
    "1",
    "0",
    "1",
    "-2097708172520403409502132772036551",
    "24677184469813106054456703134649298266936931229498"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 241.79206344620934,
  "faltings_height": 18.182593221478918,
  "conductor": "1101143210509046379320062209869918451783745022537012850",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "79",
    "89",
    "97",
    "191",
    "241",
    "337",
    "347",
    "383",
    "1223",
    "1579",
    "2543",
    "4271",
    "12619",
    "31219"
  ],
  "discriminant": "327693377652947914688669850046473878020134882226082363512262698305954117765026315172008391228680250000",
  "regulator": "5043984268414812.1876004866961760109240822634316868881025676776465368",
  "points": [
    [
      "147940940627910696",
      "54334638079566033152126761"
    ],
    [
      "226829553240477914832/5041",
      "-1655435331759255639209456747254/357911"
    ],
    [
      "179634219471368411232/841",
      "-2354714242417186854979330292146/24389"
    ],
    [
      "2438744241800850969/64",
      "138323365469663976186813857/512"
    ],
    [
      "324554606471602578288/169",
      "-5845327917726600122017923378083/2197"
    ],
    [
      "8323183823369418363927/22201",
      "-753827738038546663592918609960536/3307949"
    ],
    [
      "-21469744512670262389088542314/51063443765161",
      "1844751616145252511017321806290500107261228504/364892679834707269909"
    ],
    [
      "2297387885068464267",
      "-3481493678545318218840028484"
    ],
    [
      "80416251768496853930560055771007/9793265468543041",
      "2742159815455930487777278324472001166501508495104/969150648710639613845089"
    ],
    [
      "30651908072873732643827440900998822/803587765037663761",
      "-288120481683419925376009205742164631426584970985576/720360637454151231703910009"
    ],
    [
      "5105378662418574712751691/3667225",
      "-11529454825512891051407930420569286156/7022735875"
    ],
    [
      "91242833567260606890007999171683/1567389716214529",
      "-620020892114025384833872199385625574495875147588/62053386762325729676417"
    ],
    [
      "11408892145574335366622/292681",
      "-231517140380544101216882169149499/158340421"
    ],
    [
      "41190391122714760585312983/222695929",
      "256657366841082859159532405231282639512/3323291348467"
    ],
    [
      "-2860883902309404890326517277/135598488169",
      "385300467786176187543947630474904224083448/49932380487888053"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-039, rational kernel x=-102020260065396217/4. 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 20:42:48",
  "updated_at": "2026-09-26 20:42:48"
}