{
  "id": 5998,
  "curve_key": "245320949728:58226827395800960",
  "ainvs": [
    "0",
    "1",
    "0",
    "-5110853119",
    "-67393864955439"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 78.67749956724305,
  "faltings_height": 4.609009800242788,
  "conductor": "934186815498928733056",
  "bad_primes": [
    "2",
    "7",
    "41",
    "113",
    "127",
    "503",
    "953",
    "32713"
  ],
  "discriminant": "6581963158660205383792705750784",
  "regulator": "261663155.83828788720749693067172308514394958770374314889",
  "points": [
    [
      "-58455",
      "5623566"
    ],
    [
      "-14816",
      "2253095"
    ],
    [
      "79984",
      "5959775"
    ],
    [
      "92368",
      "15767215"
    ],
    [
      "126409",
      "36145310"
    ],
    [
      "233368",
      "107001485"
    ],
    [
      "-1030424/25",
      "1069759999/125"
    ],
    [
      "3784573/36",
      "5098514795/216"
    ],
    [
      "559551856/225",
      "13230617880079/3375"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "The rationally 2-isogenous partner of [0,1,0,-40339155689,3072117231780391] from Michael Rubinstein’s elliptic-curves-by-rank repository, torsion_Z2.add_2026-10-24.part3.tsv.gz, data row 544799.\r\n\r\nReduction gives the global minimal model [0,1,0,-5110853119,-67393864955439]. 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 18:04:24",
  "updated_at": "2026-10-27 18:04:24"
}