{
  "id": 4762,
  "curve_key": "708119686161216:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-14752493461692",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 102.58090273075658,
  "faltings_height": 6.616648972537872,
  "conductor": "48363569630503379882556192",
  "bad_primes": [
    "2",
    "3",
    "7",
    "23",
    "71",
    "113",
    "281",
    "1129"
  ],
  "discriminant": "205483174490329023755553842685251346296832",
  "regulator": "307222989.497645174191965739370305318630605517613749152",
  "points": [
    [
      "-3136803",
      "3925683243"
    ],
    [
      "-22862",
      "580740524"
    ],
    [
      "13821712",
      "49361840632"
    ],
    [
      "-2353765564428/1274641",
      "6586039283570524548/1439069689"
    ],
    [
      "-14991144027/6889",
      "2669588449052391/571787"
    ],
    [
      "-475712496/841",
      "69685038798984/24389"
    ],
    [
      "-22862/9",
      "5226756164/27"
    ],
    [
      "64336441/4",
      "501112753037/8"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + a x with a = -14752493461692. Source: Aguirre, Castaneda, Peral, 'High rank elliptic curves of the form y^2=x^3+Bx', Rev. Mat. Complut. 13 (2000) 17-31, https://revistas.ucm.es/index.php/REMA/article/view/REMA0000120017A.",
  "created_at": "2026-10-20 21:28:59",
  "updated_at": "2026-10-20 21:28:59"
}