{
  "id": 3634,
  "curve_key": "1082248451764155370596496:-123580775648981515932666683688201547456",
  "ainvs": [
    "0",
    "1",
    "0",
    "-22546842745086570220760",
    "143033305149276646344856595782381908"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "naive_height": 175.41991668778317,
  "faltings_height": 12.676011952674497,
  "conductor": "11537416688626259646150573805118160",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "19",
    "59",
    "73",
    "101",
    "103",
    "107",
    "137",
    "179",
    "881",
    "1579",
    "1979",
    "2459"
  ],
  "discriminant": "-8837349834392469949566678205035845402057412418912505963397675421908480000",
  "regulator": "62325001360551.391531546881102116772510966796813428818874386716",
  "points": [
    [
      "104903799646",
      "376593284277452880"
    ],
    [
      "-270698040591600463634/672313041",
      "5137014128691421509481810751120/17432404840089"
    ],
    [
      "-30943077278197049684/129709321",
      "542449701074924114594899355370/1477259456869"
    ],
    [
      "-26667086420967130658/57592921",
      "101757046409328853507865226480/437072677469"
    ],
    [
      "-4527259607401088189/18190225",
      "28317511515842396816420154384/77581309625"
    ],
    [
      "-49786524092343641/97969",
      "4675711847224476841663650/30664297"
    ],
    [
      "-13920530530152074/25921",
      "66747725285940548067240/4173281"
    ],
    [
      "2878265104830937/1024",
      "154694088218828092949091/32768"
    ],
    [
      "20054677157801854/49",
      "2840033637034625535870960/343"
    ],
    [
      "28208602212434254/12769",
      "4758191317875770685670320/1442897"
    ],
    [
      "1272178773606290854/17530969",
      "27638550757058300754571838280/73402167203"
    ],
    [
      "10362707801212530784324/352425529",
      "1054885779006612965798891473557270/6616084455917"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = 176 of the rank-9 fibration of X400, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #802 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:23:43",
  "updated_at": "2026-09-29 19:23:43"
}