{
  "id": 3547,
  "curve_key": "6202260831546548943121:-488078137403128375649594252617465",
  "ainvs": [
    "1",
    "0",
    "0",
    "-129213767323886436315",
    "564905251613223361576706515281"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 150.5376024861201,
  "faltings_height": 10.30889381151341,
  "conductor": "589032177631665151529373868401860082",
  "bad_primes": [
    "2",
    "3",
    "17",
    "59",
    "157",
    "257",
    "307",
    "593",
    "619",
    "827",
    "1543",
    "1723",
    "3779"
  ],
  "discriminant": "213278915439541058506596068114253282279364963834650656243712",
  "regulator": "140715305666036.1841728059529924850433253354550611167074653549001",
  "points": [
    [
      "6299421426",
      "30186131983893"
    ],
    [
      "6406603398",
      "6333504477849"
    ],
    [
      "7828713918",
      "182039525555409"
    ],
    [
      "37488461598",
      "6957465875974449"
    ],
    [
      "673335374814",
      "552440345912447985"
    ],
    [
      "-63576691506/25",
      "117064383759934893/125"
    ],
    [
      "985705098126/121",
      "306122190400048131/1331"
    ],
    [
      "1038496939704/169",
      "118893580243876827/2197"
    ],
    [
      "1559104068250/9",
      "1942669141230772543/27"
    ],
    [
      "1706954577230/289",
      "432907237427435137/4913"
    ],
    [
      "600867490752414/625",
      "14727791200831530528537/15625"
    ],
    [
      "3284899250810814/516961",
      "7534282540208674669695/371694959"
    ],
    [
      "97099352086957278/15358561",
      "1580853993493498477860927/60190200559"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "Z/2Z curve from the Fermigier 2-torsion construction (Dujella, Proc. Japan Acad. 78 (2002)), parameter s = 5*13*457 = 29705, each factor a sum of two squares (5 = 1^2+2^2, 13 = 2^2+3^2, 457 = 4^2+21^2); normalized model y^2 = x^3 + 76960218985x^2 - 93128508442464837632x, where a2 = s*17*257*593. Rank exactly 13 by 2-descent: 13 independent points, 2-Selmer upper bound 13, both with the supplied points and with no seeded points. Torsion Z/2Z, root number -1.",
  "created_at": "2026-09-28 05:49:19",
  "updated_at": "2026-09-28 05:49:19"
}