{
  "id": 2523,
  "curve_key": "577371249:13873130850807",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-12028568",
    "-16053857269"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 60.52198809014894,
  "faltings_height": 2.6896712152826203,
  "conductor": "18810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19"
  ],
  "discriminant": "4230728595002250000",
  "regulator": "9.552825382243724226315623904860173623623",
  "points": [
    [
      "-488051505/243049",
      "157187315029/119823157"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational full 2- and 3-torsion family at (p,q)=(-15,4); Velu quotient by rational order-3 subgroup. The mapped rank >=1 witness is non-torsion by the original exact 2-descent Kummer certificate and finite isogeny kernel. Conductor N=18810; local exponents {'2': 1, '3': 2, '5': 1, '11': 1, '19': 1}.",
  "created_at": "2026-09-26 20:06:54",
  "updated_at": "2026-09-26 20:06:54"
}