{
  "id": 4770,
  "curve_key": "-705855274041037480995949200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "14705318209188280854082275",
    "0"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 185.46435736217995,
  "faltings_height": 13.523603525156489,
  "conductor": "30755041227873340789321920108558919243453506727200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "23",
    "41",
    "47",
    "149",
    "157",
    "433",
    "967",
    "1033",
    "8573"
  ],
  "discriminant": "-203518200506661963938068936541957059295633128584811935369651194232651171000000",
  "regulator": "6223581569868.4046405347561169735024187140823387390060623396253",
  "points": [
    [
      "70283712595185/16",
      "-782160378242464718775/64"
    ],
    [
      "1512279300385/4",
      "18954559846587001175/8"
    ],
    [
      "2019469851315",
      "6158966376302652150"
    ],
    [
      "3712356096535585/6241",
      "1475635708760395281769450/493039"
    ],
    [
      "157351802491843065/90601",
      "151293680993523885994398150/27270901"
    ],
    [
      "2335396509025",
      "6861499898380881850"
    ],
    [
      "1896413333936326960/77841",
      "-2643710532687591534844576300/21717639"
    ],
    [
      "1021486650468435",
      "32647663331556118244550"
    ],
    [
      "6567622476950065/6724",
      "-2156346771080285891554975/551368"
    ],
    [
      "709340625665945100/208849",
      "901053046039007942274748950/95443993"
    ],
    [
      "49086645564000960/9409",
      "-13497322809659653028071800/912673"
    ],
    [
      "4120354715760241/576",
      "-300092110267293249137911/13824"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + a x with a = 14705318209188280854082275 (2-isogenous model of the curve listed there). Source: 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/.",
  "created_at": "2026-10-20 21:29:30",
  "updated_at": "2026-10-20 21:29:30"
}