{
  "id": 2748,
  "curve_key": "15202042991794196246597170268466732315121:-3544676495015988259026454242044571046329516682889818359876169",
  "ainvs": [
    "1",
    "0",
    "0",
    "-316709228995712421804107713926390256565",
    "4102634832194430855328299974024166379582894591998979469217"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 278.84110495753526,
  "faltings_height": 21.279958196145618,
  "conductor": "244375491477491983033103910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "31",
    "37",
    "41",
    "79",
    "139",
    "101119",
    "6272219"
  ],
  "discriminant": "-5238140755504586562007518355137425452716584421467159549978367183198776223910511724358470002723210127655033041715200000",
  "regulator": "473614.1819781330615558096617411825239228104884",
  "points": [
    [
      "6549660766270349842",
      "48054807623657732137411002775"
    ],
    [
      "118020126699863866269826/27321529",
      "-9145690681381380222360495785537054976011/142809632083"
    ],
    [
      "103556388136794606782554/63001",
      "-947013432357845045891383183425006547/15813251"
    ],
    [
      "64098390919985945531494308370890123631913139988088875673679728212967654143354570239814/1761925559294187155984837360322848519497467246435221195596960062121",
      "471989792300002435042372840062665712203520756307555034367990943910785778734006187171223099664131391183449040700319058201777110683/2338736714899638678778698812701839233678418950759085431813172729705797760171657198563577841458930581"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z10-009, rational kernel x=178913345320035258735/4. 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 20:20:32",
  "updated_at": "2026-09-26 20:20:32"
}