{
  "id": 3196,
  "curve_key": "8365553905025906111581808881:-4692218183563116847477583952663140232853705",
  "ainvs": [
    "1",
    "0",
    "0",
    "-174282373021373043991287685",
    "5430808082827667012901303719680524143681"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 196.50895867329132,
  "faltings_height": 14.433132266810325,
  "conductor": "391512260772660933912887936166035719203490447158",
  "bad_primes": [
    "2",
    "3",
    "13",
    "19",
    "41",
    "47",
    "107",
    "109",
    "113",
    "191",
    "263",
    "619",
    "769",
    "2953",
    "5197",
    "36527",
    "135511"
  ],
  "discriminant": "-12402470585516637860273394618549183945215593924901728307209792730412441255292048128",
  "regulator": "4780132266967.74407786177663697260941044119545368540233956296429725",
  "points": [
    [
      "32835154160018",
      "187374885582331738199"
    ],
    [
      "-6630649537874",
      "-79340361623056087217"
    ],
    [
      "3126313902698",
      "-70117779370290614761"
    ],
    [
      "9977581951946",
      "68448377567781264983"
    ],
    [
      "-1696403676689974/121",
      "-95224889527438684146827/1331"
    ],
    [
      "2131642264914346",
      "98415447602984050964671"
    ],
    [
      "-35295347848676306688662760338110/2314867957519194169",
      "-237401582484645230881086020183760490427279446037/3521999866552054280863785197"
    ],
    [
      "682617871641452/3721",
      "-16677840646644579779734111/226981"
    ],
    [
      "1348115833078618/289",
      "-337510155738676543135993/4913"
    ],
    [
      "159968948136207806/25",
      "63981233877457907054155831/125"
    ],
    [
      "1427381586367812674802764/6193847401",
      "-1702915211302481680759266081072349229/487461984306101"
    ],
    [
      "35827169063794981896010286/719648519041",
      "-211607133187395642179909400493937379569/610492951321380161"
    ],
    [
      "15493521944474",
      "-80310456658940643409"
    ],
    [
      "5673527892304967348272250/103697524441",
      "-13343456419578521178719996638596487549/33392780518015261"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-062, rational kernel x=10425279415922. 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 20:42:08",
  "updated_at": "2026-09-26 20:42:08"
}