{
  "id": 2782,
  "curve_key": "12731722574965189617646051115359124529121:884076949031588187601396887492403973332579643080229514995375",
  "ainvs": [
    "1",
    "0",
    "0",
    "-265244220311774783700959398236648427690",
    "-1023237209527301143079276008512559904813713796010727085404"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 277.0347460390866,
  "faltings_height": 21.126086565832196,
  "conductor": "6284587191562249335065454",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "41",
    "61",
    "179",
    "337",
    "649849",
    "7302509"
  ],
  "discriminant": "742001691737077980814500910427439852570838488588001297225479464066886644323752102738739537264581635137468346647974912",
  "regulator": "2892478.507967348808151991154822154412702966770",
  "points": [
    [
      "7085448708090433931272044769943119774886/12406243590199543681",
      "-596174217467169905754008935655820609172861122627772404486074/43697888892675432378697620671"
    ],
    [
      "-725360691080955975489626553603344560778974/112114119122601802215025",
      "-771192105116046496544144901983004428527724322717952968667955716/37539671123951744228967170401456375"
    ],
    [
      "-14116118448043896869115616037581597738756/1392965478007019169289",
      "-1298695113386089151656149053775743538784060494331114144269194/51988888211617723988013627716837"
    ],
    [
      "-5736790445530634923095116212430541547064506/460751281989727522795369",
      "-5843378270241171264973743455023364952837188777360856399170959042/312751807568090406804067126784211403"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z10-006, rational kernel x=6914743098109976052. 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 20:22:13",
  "updated_at": "2026-09-26 20:22:13"
}