{
  "id": 4379,
  "curve_key": "13667685934288:-50528056547896660160",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-284743456964",
    "58481641844921604"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 90.73816641522424,
  "faltings_height": 5.212865050980397,
  "conductor": "24863086248",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "37",
    "83",
    "337"
  ],
  "discriminant": "67305174902942076402707455674624",
  "regulator": "8483.206756019629049511093124385615116406070914",
  "points": [
    [
      "7685890/9",
      "17871524216/27"
    ],
    [
      "16055250/49",
      "6511173864/343"
    ],
    [
      "128277085/324",
      "-515292553009/5832"
    ],
    [
      "52941441970/136161",
      "4065959364797512/50243409"
    ]
  ],
  "submitter": "Volkan Dagli",
  "history": [],
  "commentary": "2-ISOG#1 torsion/torsion_Z4.tsv.gz:352 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.",
  "created_at": "2026-10-17 10:06:53",
  "updated_at": "2026-10-17 10:06:53"
}