{
  "id": 5360,
  "curve_key": "19855958476071470868739394030227009:-2798198479405422942129882387555791135715752472927073",
  "ainvs": [
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  "rank_lower_bound": 12,
  "torsion": [
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  ],
  "family": null,
  "families": [],
  "naive_height": 236.9216311051888,
  "faltings_height": 17.438231570887783,
  "conductor": "165048118968436491259413491400640254451352730",
  "bad_primes": [
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    "3",
    "5",
    "7",
    "13",
    "31",
    "37",
    "83",
    "89",
    "103",
    "211",
    "331",
    "449",
    "5016621163",
    "62909039502787"
  ],
  "discriminant": "-881174648137977236354532620412342886556308875437861803738437619494916056573590000117515535155200",
  "regulator": "1062940042411803.3845625651514441766912300239641968866638735342",
  "points": [
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      "113681266649304678096121784/9060945721",
      "-132467896919115928182478816466118048380/862502362236269"
    ],
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      "17125948887340984805058252515/1443232211716",
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      "-157961059868409683074714713716860208/3083448003875"
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      "1724733857917502339534998777811541194/146752713349809071761",
      "-31726707800909992726810703160663818442181275074936294/1777784885935149069868443361991"
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      "491649357026066136460990447640/76219377797641",
      "609404765092079462573114909020699098747957820/665423445562568854811"
    ],
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      "21106007004081832172/1849",
      "5068818094719688616450696432/79507"
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      "156585082345078744864418/3279721",
      "-57068399952613580140089805378060544/5939574731"
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    [
      "246927709038243966754088/23049601",
      "-21163628366992124854014287200889884/110661134401"
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  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "t = 8357/1771 for y^2 + (7t^2+309) x y - 91 (t^2-1)(t^2-25)(t^2-121) y = x^3 from https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/main/submission/board/3-r12-z3k3.ec",
  "created_at": "2026-10-21 19:53:29",
  "updated_at": "2026-10-21 19:53:29"
}