{
  "id": 2850,
  "curve_key": "11483870720555232346119748680961:-39093085216454152017739459410246687153639431041",
  "ainvs": [
    "1",
    "0",
    "0",
    "-239247306678234007210828097520",
    "45246626407933026379552521501618249969926400"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    7
  ],
  "naive_height": 214.56454957479954,
  "faltings_height": 15.712010869489722,
  "conductor": "36234340651501462470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "89",
    "713545091839"
  ],
  "discriminant": "-7977217740530782168811753192612927591247152432589415308725010668402717491200000000000000",
  "regulator": "34781.4904553574930476442132241342568795714181909",
  "points": [
    [
      "46074969993440",
      "5858423537724469003280"
    ],
    [
      "275652423665370",
      "492718372260784145100"
    ],
    [
      "138768613071840",
      "3836513831575606436880"
    ],
    [
      "297508887793440",
      "633557750590112003280"
    ],
    [
      "169967679183690",
      "3080992491904517095530"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Elkies (2006). Source: https://dujella.github.io/tors/z7old5.html (curve entry 5). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:25:15",
  "updated_at": "2026-09-26 20:25:15"
}