{
  "id": 1082,
  "curve_key": "37736205001:-7330559140223749",
  "ainvs": [
    "1",
    "0",
    "1",
    "-786170938",
    "8484377935088"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    12
  ],
  "naive_height": 73.06165744625515,
  "faltings_height": 3.6424345938260525,
  "conductor": "278070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "23",
    "31"
  ],
  "discriminant": "33222494634354492187500",
  "regulator": "4.252962695109764646180575214514066619399",
  "points": [
    [
      "16198",
      "-7612"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 278070s4 = LMFDB 278070.s2: https://www.lmfdb.org/EllipticCurve/Q/278070/s/2\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 278070, minimal discriminant 33222494634354492187500, torsion ℤ/12ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-23 15:26:10",
  "updated_at": "2026-09-23 15:26:10"
}