{
  "id": 2721,
  "curve_key": "67402782005316512978222612096990876165983010827566721:-17499141099372053679735023049169048375545876892519238105531352257886413454264769",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1404224625110760687046304418687309920124646058907640",
    "20253635531680617684878498782482494638392485445816342546348423621425806959392"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 364.92757810741807,
  "faltings_height": 27.821858908980097,
  "conductor": "465432724185682885970875984683390",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "31",
    "43",
    "61",
    "281",
    "1663",
    "3019",
    "101159",
    "913829429"
  ],
  "discriminant": "171667838884538273419042671054119499692229395395414093164193308574069369346159466907191742659542800695303049038727193007621720073944826985718900000",
  "regulator": "84054986.12375643244574374213703130227394729291",
  "points": [
    [
      "4541052312445649565550702379938733/208167184",
      "-4347141328674606170092020527091849549791989758139/3003436130752"
    ],
    [
      "9634825434006232487125421644277163430410093523046120666/438160222462278765651980401009",
      "-829972605598108603917541990246483148648135259900944047475346711533671730436962174/290034340881005502277800486723328668218960777"
    ],
    [
      "12511165309045337662878782934913922130146766494516695591710465341925845384809198175381470210607102432227615860035837491808552349887125170540322955306158294743975283363283061797580719960311/575208145429843294201829059191943864728957574714518379900750294665599611319924446677345925559870917647717683755197854455555156507105905058259831474173512394978404",
      "-406777212681082144988154419380598628312549115676141107962686898236099604343601043299453371818931905219768445229248150671124636762387409768283922337559588441289913148390339646851258581541018100968357228606346456462059338356249828991321539178208116392789478976587054162360175696481/436252110587491091954646404080333091813438407349517463917485847324138342069580387397250674512109247938281415167156289332118014207974401484933887751869171460928496730898270981333481842048607019050916546334074423999800080299660354241045523165208"
    ],
    [
      "12205418912651372509317738292422313864384515557305314614051245458139038284/564094612319404242590850464394840174706060493521",
      "-7203234375051574914212748139841505075499988337540583334743877298970854159021135394484642326207319256009968/423670209653486612120790401160727523390286083688990668399689456404841319"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z10-025, rational kernel x=-10817324679410223564373776. 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 20:19:20",
  "updated_at": "2026-09-26 20:19:20"
}