{
  "id": 4591,
  "curve_key": "51785908584188919769579477081:-11771713797244247778863051910468709169341021",
  "ainvs": [
    "1",
    "0",
    "1",
    "-1078873095503935828532905773",
    "13624668746810382060185388457278998611256"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 198.35074676412646,
  "faltings_height": 14.306128219851358,
  "conductor": "937937625235846068118709835889853830",
  "bad_primes": [
    "2",
    "5",
    "7",
    "13",
    "47",
    "53",
    "89",
    "101",
    "211",
    "1123",
    "575212549",
    "337720088071"
  ],
  "discriminant": "176611793261384048424478841035871534552430271729164647141571086687390792843750000",
  "regulator": "572211760511.3225781387875034401757552594997490893585806657",
  "points": [
    [
      "26869333462010895",
      "-4404382382025142110090698"
    ],
    [
      "6259891776802361116655/320159449",
      "-12710369079935690909400123790486/5728613020957"
    ],
    [
      "968520045912364535/49729",
      "-2820765602047827469410566/11089567"
    ],
    [
      "2240534311702865440455/42601729",
      "-88959632144623270316890718153734/278061485183"
    ],
    [
      "208823623451263561193998535/905909914849",
      "2988556762527764531821484993266181859814/862238715583874257"
    ],
    [
      "13175510710844483/529",
      "571203537444268065306398/12167"
    ],
    [
      "2411662280405145093670/119661721",
      "-10737391548718414117823123864762/1308979566019"
    ],
    [
      "1641775500168070/81",
      "6686377160946661907983/729"
    ],
    [
      "47767897702797745/576",
      "9721158139606698903939973/13824"
    ],
    [
      "331246613860492749343030/16946051329",
      "-4713028938094815164835985272584409/2205986123855233"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "t = 17/228 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": "2026-10-18 15:15:26",
  "updated_at": "2026-10-18 15:15:26"
}