{
  "id": 5088,
  "curve_key": "1608958302856240466880974989688961969:-2051049487099148873500772030188382816461281187933554153",
  "ainvs": [
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    "-1",
    "1",
    "-33519964642838343060020312285186708",
    "2373899869327718611968847677131325135909338705479031"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    3
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  "family": null,
  "families": [],
  "naive_height": 250.1158932575122,
  "faltings_height": 18.678416107244324,
  "conductor": "1242428825390939691392468726268105015400663549890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "29",
    "37",
    "41",
    "79",
    "173",
    "509",
    "617",
    "4091",
    "6367",
    "116201",
    "351529",
    "167683603"
  ],
  "discriminant": "-24084668962373785968456972345263040447034191898777114920601832671018286783956200562069775323556400230400",
  "regulator": "7894877304163844.6441887863900360117169602506356949641717529757",
  "points": [
    [
      "30132647849878073937/289",
      "-17318034341235381005592397495/4913"
    ],
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      "6304621253763744516345595857/61735850089",
      "-60959620332514625994563993201978197151465/15339321464063563"
    ],
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      "36475881073774046348042514192399/198203402011729",
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      "909137062803733551368585398687/9565269571729",
      "201914578717057423542200489714377866165388725/29583245730243301433"
    ],
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      "259021344724276615799517005170293/1320126928269601",
      "-2776444548630987437418112510606407682232814152845/47964899074756889683151"
    ],
    [
      "48765521673382641918343831/211818916",
      "255319774201401950732996425664594494839/3082812503464"
    ],
    [
      "13473464338366433084409/107584",
      "417842982834401889029721122061937/35287552"
    ],
    [
      "12832142631558573798807/151321",
      "699458924141814459597747857005289/58863869"
    ],
    [
      "-109814651154186466503/529",
      "-239226327793364211603900579433/12167"
    ],
    [
      "86077370831720891842718927109/761216115529",
      "3602326594124378459939699125815879867829721/664143552828395333"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "t = 8643/3365 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 02:27:19",
  "updated_at": "2026-10-21 02:27:19"
}