{
  "id": 4654,
  "curve_key": "7678619353:-622061603177885",
  "ainvs": [
    "1",
    "1",
    "0",
    "-159971236",
    "719912052700"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 68.28511678860097,
  "faltings_height": 3.6502023465641793,
  "conductor": "495488867460190302",
  "bad_primes": [
    "2",
    "3",
    "73",
    "79",
    "97",
    "109",
    "457",
    "1487",
    "1993"
  ],
  "discriminant": "38067092677556711716837284",
  "regulator": "97498.5942909570826620368261395945116613513442408033274",
  "points": [
    [
      "-38",
      "852070"
    ],
    [
      "4423",
      "312289"
    ],
    [
      "11858",
      "-706306"
    ],
    [
      "4618",
      "279958"
    ],
    [
      "126357",
      "-44761655"
    ],
    [
      "10371",
      "-425263"
    ],
    [
      "-37517/9",
      "31010411/27"
    ],
    [
      "-2729",
      "1067272"
    ]
  ],
  "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. Eight supplied rational points checked exactly on the displayed model. Rational torsion Z/2Z. Source-attributed existing curve.",
  "created_at": "2026-10-20 17:37:30",
  "updated_at": "2026-10-20 17:37:30"
}