{
  "id": 4321,
  "curve_key": "85195103177260201356016:-23467873829305464602915160944438936",
  "ainvs": [
    "0",
    "-1",
    "1",
    "-1774897982859587528250",
    "27161891006732216692105002491406"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    5
  ],
  "family": null,
  "families": [],
  "naive_height": 158.3976927318396,
  "faltings_height": 11.145052854533633,
  "conductor": "5886444423733736980645",
  "bad_primes": [
    "5",
    "11",
    "19",
    "43",
    "59",
    "107",
    "179",
    "115925634521"
  ],
  "discriminant": "39133375789501649216531428085233976313021291701839519468105403125",
  "regulator": "599366.0262130618575958628425895546044041731319068033",
  "points": [
    [
      "9597604695",
      "3318312177071402"
    ],
    [
      "52651304925/4",
      "19725814118996421/8"
    ],
    [
      "-11942476868459/625",
      "114926082737125159536/15625"
    ],
    [
      "138517715575/9",
      "50443432097669999/27"
    ],
    [
      "7881198559825/144",
      "16750232084940697711/1728"
    ],
    [
      "35192515738057/841",
      "124755515212508903271/24389"
    ],
    [
      "5233853624097975/279841",
      "105548385753774718145418/148035889"
    ]
  ],
  "submitter": "Volkan Dagli",
  "history": [],
  "commentary": "Curve 5-7.ec from Layr Labs / Yukon Elliptic Rank Challenge with conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.",
  "created_at": "2026-10-17 09:50:28",
  "updated_at": "2026-10-17 09:50:28"
}