{
  "id": 4697,
  "curve_key": "19113601:-82624158305",
  "ainvs": [
    "1",
    "1",
    "1",
    "-398200",
    "95463896"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 50.29773220151667,
  "faltings_height": 2.061738859747483,
  "conductor": "1274102071359",
  "bad_primes": [
    "3",
    "13",
    "23",
    "79",
    "277",
    "4993"
  ],
  "discriminant": "90286695082712817",
  "regulator": "687.71751322010434229809890105732808797503607590445",
  "points": [
    [
      "-632",
      "10072"
    ],
    [
      "694",
      "12061"
    ],
    [
      "-502",
      "13257"
    ],
    [
      "1292",
      "41064"
    ],
    [
      "1343",
      "43884"
    ],
    [
      "96",
      "7576"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. I checked the six supplied rational points exactly on this minimal model. The source records rank 6 with independent points and a matching 2-descent upper bound. Rational torsion Z/2Z. Source-attributed existing curve.",
  "created_at": "2026-10-20 20:50:28",
  "updated_at": "2026-10-20 20:50:28"
}