{
  "id": 3177,
  "curve_key": "1719465222267493641911064686219515628132401:-2254797707400535736555633465915888327289003245117169754443858601",
  "ainvs": [
    "1",
    "0",
    "0",
    "-35822192130572784206480514296239908919425",
    "2609719568750620065454923921391767461604324824175741297455625"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    3
  ],
  "naive_height": 291.75184223817126,
  "faltings_height": 21.98060472083012,
  "conductor": "5751679256865023413274743068599885347967822805404077230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "31",
    "37",
    "41",
    "43",
    "47",
    "53",
    "59",
    "61",
    "187172595299",
    "7081017707425445923"
  ],
  "discriminant": "-236970537685396512783717319019850371091109730207165202086609487218990930925405052043298511702129909327649698787328000000",
  "regulator": "310174806765.2842701719428032201676966654328826876068450587674922",
  "points": [
    [
      "111765301087195517610",
      "46430435456204326675146597675"
    ],
    [
      "111116582336682124050",
      "34996683196066023464195962875"
    ],
    [
      "111913032824849252130",
      "49063192420997854527679793475"
    ],
    [
      "110123909838304503990",
      "18512376609554805482691445335"
    ],
    [
      "109146709187032115370",
      "10506129421757959855129586475"
    ],
    [
      "110382143345238886970",
      "22567063509763234684093270475"
    ],
    [
      "110245179394644403100",
      "20382223547410442956289336075"
    ],
    [
      "108522553923729999720",
      "17018033523451040060797113555"
    ],
    [
      "108512500742043656106",
      "17163334387154750309786061867"
    ],
    [
      "109741057847530716000",
      "13297340647117901361820923075"
    ],
    [
      "108902034932485796850",
      "12260441074498263650721717075"
    ],
    [
      "110291739877102075140",
      "21117334974942773428569817185"
    ],
    [
      "111294342929434080810",
      "38103895579546047175336101675"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Eroshkin (2009). Source: https://dujella.github.io/tors/z3old891011121314.html (curve entry 7). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:41:00",
  "updated_at": "2026-09-26 20:41:00"
}