{
  "id": 6047,
  "curve_key": "144849136:-2007735214616",
  "ainvs": [
    "0",
    "-1",
    "1",
    "-3017690",
    "2324773506"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    5
  ],
  "family": null,
  "families": [],
  "naive_height": 56.656056887663944,
  "faltings_height": 2.7073462820136633,
  "conductor": "45464315",
  "bad_primes": [
    "5",
    "13",
    "29",
    "89",
    "271"
  ],
  "discriminant": "-574005521797503696875",
  "regulator": "28.061609096185348694964419141845315748014267",
  "points": [
    [
      "-2028",
      "9990"
    ],
    [
      "390",
      "34742"
    ],
    [
      "56030",
      "13256262"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained in my own rational-parameter search of the Tate X_1(5) family, following the construction described by David Renshaw on curve#1185 and curve#1186. The family is y^2+(1-t)*x*y-t*y=x^3-t*x^2, specialized at t=-65/29. Clearing denominators with x=X/29^2 and y=Y/29^3 gives [94,1885,54665,0,0]; the displayed equation is its global minimal model, with discriminant -574005521797503696875. All three listed rational points were checked exactly and returned as an independent set, with rank bounds [3,3]. The rational torsion subgroup is Z/5Z.",
  "created_at": "2026-10-28 17:03:22",
  "updated_at": "2026-10-28 17:03:22"
}