{
  "id": 4986,
  "curve_key": "-29035538891599270800:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "604907060241651475",
    "0"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 134.44515669784036,
  "faltings_height": 9.272003469794855,
  "conductor": "468368065958652117289244717273184800",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "19",
    "23",
    "47",
    "73",
    "229",
    "613",
    "1493"
  ],
  "discriminant": "-14165957494505808390700888235053621088485554243379000000",
  "regulator": "234917979030.095295349434557145588566038938178883021915075575",
  "points": [
    [
      "2707655531",
      "146590523489746"
    ],
    [
      "5584119209",
      "421312284729902"
    ],
    [
      "14728762475",
      "1790004158911150"
    ],
    [
      "64057253771",
      "16213787730992894"
    ],
    [
      "6483340556/169",
      "10596394496418346/2197"
    ],
    [
      "8685878355/361",
      "26179787467599150/6859"
    ],
    [
      "9431228745/4",
      "964453170178275/8"
    ],
    [
      "114579590755/9",
      "38857049242483850/27"
    ],
    [
      "1860950287449/38416",
      "40838013762168182307/7529536"
    ],
    [
      "2315212172009/71824",
      "85071089078804015627/19248832"
    ],
    [
      "330753855368475/4133089",
      "58770365094917229565350/8402569937"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + 604907060241651475 x: the curve y^2 = x^3 + 4Bx (2-isogenous to y^2 = x^3 - Bx), reduced mod 4th powers, where B = B(89,102,168,214) is the parametrization of Aguirre, Castaneda and Peral (Aguirre, Castaneda, Peral, 'High rank elliptic curves with torsion group Z/(2Z)', Math. Comp. 73 (2004) 323-331, doi:10.1090/S0025-5718-03-01547-3, https://www.ams.org/mcom/2004-73-245/S0025-5718-03-01547-3/). Found by a Mestre-Nagao sieve over all quadruples a1<a2<a3<a4 with a1^2+a2^2+a3^2+a4^2 < 3*10^5.",
  "created_at": "2026-10-21 01:12:08",
  "updated_at": "2026-10-21 01:12:08"
}