{
  "id": 45,
  "curve_key": "26914364817703967532575697223238202217921:-4578705818068316799984129290405535142567907177009541961541281",
  "ainvs": [
    "1",
    "0",
    "0",
    "-560715933702165990261993692150795879540",
    "5299428030171662962897867758309003693598430128674403539600"
  ],
  "rank_lower_bound": 13,
  "naive_height": 279.3530439307271,
  "faltings_height": 21.202075126528637,
  "conductor": "37782801949200843416322963769043529248461782217859568090",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "31",
    "37",
    "41",
    "43",
    "47",
    "53",
    "59",
    "61",
    "113",
    "197",
    "317",
    "3313949",
    "2831657657",
    "4864617187"
  ],
  "discriminant": "-849674615711570771215349016224804046891153693433134502714153993581965535857133434327195120355094716597801586176000000",
  "regulator": "473362182709.7477529528683850131310786537924858078223167486334695",
  "points": [
    [
      "30978765264695144680",
      "132887030666136666891811891660"
    ],
    [
      "42714959134973152720",
      "243484714136201166251098454860"
    ],
    [
      "17517044808100174120",
      "29195754303760059255051062860"
    ],
    [
      "14407536544275712180",
      "14545360491234198754332073660"
    ],
    [
      "27024189809840210680",
      "99410687206608213450615379660"
    ],
    [
      "15223373261754620200",
      "17072594325815595384787766860"
    ],
    [
      "-19625425810319741720",
      "93513850432355415588023731660"
    ],
    [
      "18799275311571587070",
      "37447008534737807545137468570"
    ],
    [
      "-18348119874544858160",
      "97008001583008247645310994660"
    ],
    [
      "16004432727240519730",
      "20612929621400491642269765910"
    ],
    [
      "-27235206268166134070",
      "19202914916421997002398631160"
    ],
    [
      "13326569619771689680",
      "13920236659741078875971506660"
    ],
    [
      "27069452184006616180",
      "99781951498337473669562238160"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Rank 13 curve due to Eroshkin (2007), listed on Dujella's high-rank elliptic curves with prescribed torsion page for torsion group Z/3Z: https://web.math.pmf.unizg.hr/~duje/tors/z3old8910111213.html. The model is y^2 + x*y = x^3 - 560715933702165990261993692150795879540*x + 5299428030171662962897867758309003693598430128674403539600, with the 13 listed integral independent points.",
  "created_at": "2026-05-28 05:18:56",
  "updated_at": "2026-07-01 22:46:37"
}