{
  "id": 3187,
  "curve_key": "2754093437705365780357807597921:-4570381465888452018588243894250543565026794385",
  "ainvs": [
    "1",
    "0",
    "0",
    "-57376946618861787090787658290",
    "5289793363296814684546397379863278967957636"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 210.27192335264965,
  "faltings_height": 15.187153001546186,
  "conductor": "3953388363442151568066959453452856637833267252586",
  "bad_primes": [
    "2",
    "3",
    "17",
    "23",
    "29",
    "31",
    "61",
    "73",
    "109",
    "241",
    "277",
    "313",
    "449",
    "653",
    "953",
    "1039",
    "1399",
    "2441",
    "16139"
  ],
  "discriminant": "865990573175423503916881419417995780536176737460523462517246143427090471689767616512",
  "regulator": "80465490717249.7168914257849924228263792381476513961736225123637355",
  "points": [
    [
      "242560674141188",
      "2375631346522482750974"
    ],
    [
      "145429899457796",
      "-145915003286519025154"
    ],
    [
      "202922314117268",
      "1415117272008187871918"
    ],
    [
      "144674017245188",
      "-130191573412088897026"
    ],
    [
      "184875226768388",
      "1000519718859597784574"
    ],
    [
      "393909487538614244/2809",
      "-5515167520590651512855834/148877"
    ],
    [
      "14122906844521940",
      "-1678124107843147915777426"
    ],
    [
      "717284942759969252/1849",
      "511641729763087998497876186/79507"
    ],
    [
      "6202429803640303076/44521",
      "146298880193863391757108266/9393931"
    ],
    [
      "-19734507309107740/121",
      "4273600604034170236254106/1331"
    ],
    [
      "636160033502414599811776276/4644701694649",
      "233255442646300923131033981384481688550/10010061370134654893"
    ],
    [
      "1495384707898374087170538212/11372899651129",
      "5248866898360613498272959988976636175398/38353659715176859117"
    ],
    [
      "395786792715416/25",
      "261766825861766998239874/125"
    ],
    [
      "959997774638785183387076/2413462129",
      "-798907597951239211859699044725386222/118566154011383"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-069, rational kernel x=-1100953370271777/4. 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 20:41:42",
  "updated_at": "2026-09-26 20:41:42"
}