{
  "id": 4694,
  "curve_key": "708625614976:-592498846572771680",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-14763033645",
    "685767474914886"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 81.8597795323037,
  "faltings_height": 4.6699488351578005,
  "conductor": "341990625678330591996",
  "bad_primes": [
    "2",
    "3",
    "11",
    "37",
    "47",
    "101",
    "157",
    "349",
    "2377",
    "3061"
  ],
  "discriminant": "2767161557783989223854566234192",
  "regulator": "322666.18191672936039684505649202685917612520100034982360",
  "points": [
    [
      "-100837",
      "33898327"
    ],
    [
      "-48519",
      "35886411"
    ],
    [
      "17415",
      "20831481"
    ],
    [
      "89043",
      "8786697"
    ],
    [
      "93931",
      "11305239"
    ],
    [
      "601719",
      "457890873"
    ],
    [
      "714325/9",
      "-101082113/27"
    ],
    [
      "53934",
      "6813402"
    ],
    [
      "63591",
      "2029191"
    ]
  ],
  "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 nine supplied rational points exactly on this minimal model. The source records rank 9 with independent points and a matching 2-descent upper bound. Rational torsion Z/2Z. Source-attributed existing curve.",
  "created_at": "2026-10-20 20:46:49",
  "updated_at": "2026-10-20 20:46:49"
}