{
  "id": 2728,
  "curve_key": "16022202790814050232349626055465329275140452245201:-64133262902216243039943510812500802324692571747418581408978797616421623449",
  "ainvs": [
    "1",
    "0",
    "0",
    "-333795891475292713173950542822194359898759421775",
    "74228313544231762777712368957403490860668082434004048855306579752017657"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 339.8941796953485,
  "faltings_height": 25.743271013576642,
  "conductor": "2987967270845792978421324415770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "37",
    "41",
    "79",
    "107",
    "1613",
    "1801",
    "97511",
    "1611289"
  ],
  "discriminant": "3514893475251583789589985767621001993912881097478087443547037308249099299962733036396071139758796633726257347707217215545988769382400000",
  "regulator": "28636914.29118202423707511267144661765735412193",
  "points": [
    [
      "247917146828997382687143720444917083275119406289/742826828116078394008576",
      "-117570329842267135422911976182807887319393955923946113738324201410103/640223145272908184070179587060301824"
    ],
    [
      "446889245784534245946136559785160475141274575167509066/1336002477617657319753548879329",
      "1441557911710121062063359576046861661990963263083419833779722878757907179272309/1544226124275244127092395420228982799256689233"
    ],
    [
      "114863167822441289348441644041707270394132480219163096348336489100831634090406/199064967457659882636721511144799522865260650041420369",
      "24117662339303375427363867136180035455898358846211606204786518097260853497750741746680162394661463662611182267718251/88816213885453375466442031170047269745155032011278792594457882959414963131319847"
    ],
    [
      "12781861363362559750597491812574986528710485769961974/39904287059765722302765462025",
      "104966716700929713259791461650878790419250363493745704135266874172559068940303/7971303301599041640078592646751861594734875"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z10-024, rational kernel x=-2668575461961110890446385/4. 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 20:19:40",
  "updated_at": "2026-09-26 20:19:40"
}