{
  "id": 3648,
  "curve_key": "59945729168790803935691671696:4213425384911698187227080376569615512924480",
  "ainvs": [
    "0",
    "1",
    "0",
    "-1248869357683141748660243160",
    "-4876649751055622525002422594205126924716"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 198.78971144966505,
  "faltings_height": 14.62884243490782,
  "conductor": "66489049159927911945099447956450941788165109722672",
  "bad_primes": [
    "2",
    "3",
    "11",
    "43",
    "59",
    "67",
    "73",
    "347",
    "787",
    "907",
    "1097",
    "2113",
    "5659",
    "21517",
    "10645571",
    "39297109"
  ],
  "discriminant": "114387414089721574790994322680274155266079235884247851872967832301241258376896909312",
  "regulator": "12412053435347711.537700615818640055311111892523115259632044286084318",
  "points": [
    [
      "-16003029846420",
      "104931961248755966622"
    ],
    [
      "-11138017107933",
      "87473122005189162396"
    ],
    [
      "-7808317302402",
      "66323802436362562080"
    ],
    [
      "1887399160320750",
      "81982156390805741994528"
    ],
    [
      "121743491764184454",
      "42478445202717796605052632"
    ],
    [
      "-25879752251231239428/2301289",
      "307245001477945283510248993590/3491055413"
    ],
    [
      "-4811400031279389/625",
      "1022360636501127748203984/15625"
    ],
    [
      "-3553826403626106/289",
      "456173382553645720202712/4913"
    ],
    [
      "-181898675677194/25",
      "7730694939400586495496/125"
    ],
    [
      "336437066233732/9",
      "701967728028195414170/27"
    ],
    [
      "1933578120393684/49",
      "29282765019897822775518/343"
    ],
    [
      "93335319290666406/2401",
      "8580428512188730511408424/117649"
    ],
    [
      "598011854981587356/361",
      "462344408670181128858396234/6859"
    ],
    [
      "9407382976931797398/121801",
      "25484006268034431464358162360/42508549"
    ],
    [
      "21659978818433618046/494209",
      "54464269435368534247761774816/347428927"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = 544 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 19:26:36",
  "updated_at": "2026-09-29 19:26:36"
}