{
  "id": 2740,
  "curve_key": "873303526853793758095799680735767776580395281:-25807612019766109453357487831226525409114530985771699770263415235321",
  "ainvs": [
    "1",
    "0",
    "0",
    "-18193823476120703293662493348661828678758235",
    "29869921319173737793236316986037320276015494544271523285414982225"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 310.4425712510934,
  "faltings_height": 23.191753168440865,
  "conductor": "230951513872748392384304490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "37",
    "97",
    "2129",
    "2311",
    "21751",
    "13700201"
  ],
  "discriminant": "1462541505135558063664188468471620315305637335655123410877608134534916306534678069319441211520063572633037916160000000000",
  "regulator": "8688163.004085452925959092779969703389949228367",
  "points": [
    [
      "497674581787641293286798666328769897219054396745124583230/96571539575500036352466173858254369",
      "8106913835245590599446838664152576520439033941641528781546419435310998594705270520895/30010534654303954438568763386496765003786461928685903"
    ],
    [
      "811697797494060056628408862816/329604025",
      "-312529898961549912894119367867471609301/5983961073875"
    ],
    [
      "36624881956695744067755428940511307856855735878330363944631073684765318430/14763997228363931516286208838045290292208423611997649",
      "2786027784200420762852982426695450129074720317189638409562001895239644459516060549607505456737761557282089495/1793931816791384351502278739211705153957846441312350276320925801239258202855143"
    ],
    [
      "117236815744058057404943512899840743064670/47918610527298187681",
      "457403475565314842072507593063676616049015020027690111200735/331708289490937450016027992079"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z10-013, rational kernel x=-1231319839060116714082. 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 20:20:10",
  "updated_at": "2026-09-26 20:20:10"
}