{
  "id": 2789,
  "curve_key": "8955541468152000399748021791727331707201:-847496218312266180713165169220358986912188267145234219000801",
  "ainvs": [
    "1",
    "0",
    "0",
    "-186573780586500008328083787327652743900",
    "980898400824382153587652612289503456380284993585235210000"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 275.9792733777233,
  "faltings_height": 20.468385422026255,
  "conductor": "733110676848154824909690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "41",
    "103",
    "157",
    "179",
    "1721",
    "5196749"
  ],
  "discriminant": "9248148920983090344884484432626968249068095014341159769335996816895345665147250324161547357644810240000000000",
  "regulator": "391794.8148281803252398215955119451296200526697",
  "points": [
    [
      "2190443304866758281055800/175561",
      "1794821617365545295688542044700789900/73560059"
    ],
    [
      "184643250697384236577751695559905334614200/7155149337470205577489",
      "69933529551170720710364761418050399826466344301740149323759300/605240600845860567175438900043513"
    ],
    [
      "59574809831349313207687050/7447441",
      "-11219328410770529568229883858556755850/20324066489"
    ],
    [
      "-2248465260103497317409480/190969",
      "3280715834147755189659157479396634260/83453453"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z10-004, rational kernel x=-63094581573040382401/4. Source: https://dujella.github.io/tors/z10.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 20:22:31",
  "updated_at": "2026-09-26 20:22:31"
}