{
  "id": 6001,
  "curve_key": "-2989746464:-275990816817280",
  "ainvs": [
    "0",
    "1",
    "0",
    "62286385",
    "319454577889"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 66.502777417382,
  "faltings_height": 3.629877305385141,
  "conductor": "533296246689681536",
  "bad_primes": [
    "2",
    "17",
    "89",
    "97",
    "167",
    "271",
    "353",
    "1777"
  ],
  "discriminant": "-59545735319715521997883648",
  "regulator": "295168.784933759635516537842979952659803150739647491790",
  "points": [
    [
      "-3351",
      "270398"
    ],
    [
      "-2280",
      "406933"
    ],
    [
      "-503",
      "536654"
    ],
    [
      "10159",
      "1414492"
    ],
    [
      "41127",
      "8511536"
    ],
    [
      "221581/100",
      "684363571/1000"
    ],
    [
      "525856/25",
      "413378179/125"
    ],
    [
      "600175/1089",
      "21380245604/35937"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "The rationally 2-isogenous partner of the rank-8 curve [0,1,0,-495993705,3489927208999] from Michael Rubinstein’s elliptic-curves-by-rank repository, torsion_Z2.add_2026-10-24.part3.tsv.gz, data row 484267.\r\n\r\nReduction gives the global minimal model [0,1,0,62286385,319454577889]. PARI/GP returned matching rank bounds [8,8] and the eight rational points listed here. All eight were checked exactly on this model. Rational torsion Z/2Z.\r\n\r\nSource:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2.add_2026-10-24.part3.tsv.gz",
  "created_at": "2026-10-27 18:12:40",
  "updated_at": "2026-10-27 18:12:40"
}