{
  "id": 5999,
  "curve_key": "325516440256:127150155208540160",
  "ainvs": [
    "0",
    "1",
    "0",
    "-6781592505",
    "-147166792022201"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 79.52603641505547,
  "faltings_height": 4.657928175864765,
  "conductor": "187638029667623179328",
  "bad_primes": [
    "2",
    "41",
    "47",
    "79",
    "83",
    "113",
    "131",
    "193",
    "241",
    "337"
  ],
  "discriminant": "10604670264513178856790892777472",
  "regulator": "20398305.221673015864112671798449599387022971186163639618",
  "points": [
    [
      "-62529",
      "5692336"
    ],
    [
      "-60225",
      "6543632"
    ],
    [
      "-44319",
      "8144836"
    ],
    [
      "-37089",
      "7303264"
    ],
    [
      "124863",
      "30867280"
    ],
    [
      "184631",
      "69961336"
    ],
    [
      "10413635",
      "33603919832"
    ],
    [
      "-1127789/25",
      "1022856384/125"
    ],
    [
      "-358865/9",
      "208873736/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rationally 2-isogenous to the rank-9 curve [0,1,0,-42104490145,3212429325415839] in Michael Rubinstein’s elliptic-curves-by-rank repository, torsion_Z2.add_2026-10-24.part3.tsv.gz (recorded source index 544625).\r\n\r\nThe source points were transported through the degree-2 isogeny to the minimal model [0,1,0,-6781592505,-147166792022201]. PARI/GP returned matching rank bounds [9,9] and the nine rational points listed here. All nine 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 18:06:58",
  "updated_at": "2026-10-27 18:06:58"
}