{
  "id": 6003,
  "curve_key": "6944279008:213690346180480",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-144672479",
    "-247278565401"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 67.98355197966234,
  "faltings_height": 3.724681409652606,
  "conductor": "251014774874769024",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "31",
    "113",
    "127",
    "1033",
    "11953"
  ],
  "discriminant": "167367175074685363173467904",
  "regulator": "351847.667612220108420044411071745457299637703273749403",
  "points": [
    [
      "-10987",
      "125820"
    ],
    [
      "-3490",
      "463797"
    ],
    [
      "-2795",
      "367748"
    ],
    [
      "-1762",
      "46485"
    ],
    [
      "14766",
      "914205"
    ],
    [
      "21997",
      "2685800"
    ],
    [
      "-523297/49",
      "96781770/343"
    ],
    [
      "-34939/4",
      "4732173/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rationally 2-isogenous to the rank-8 curve [0,-1,0,-1255942889,16958965700793] in Michael Rubinstein’s elliptic-curves-by-rank repository, torsion_Z2.add_2026-10-24.part3.tsv.gz, source index 484153.\r\n\r\nThe source points were transported through the degree-2 isogeny to the minimal model [0,-1,0,-144672479,-247278565401]. Using these points, PARI/GP returned matching rank bounds [8,8] and the eight independent points listed here. All eight were checked exactly on this model. Rational torsion Z/2Z.\r\n\r\nSource: https://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2.add_2026-10-24.part3.tsv.gz",
  "created_at": "2026-10-27 18:26:28",
  "updated_at": "2026-10-27 18:26:28"
}