{
  "id": 4768,
  "curve_key": "-62030049842453214128002704:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "1292292705051108627666723",
    "0"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 178.16898352309062,
  "faltings_height": 12.915655705232375,
  "conductor": "5937850437433996936516077156029887017540129986592",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "23",
    "47",
    "67",
    "103",
    "127",
    "149",
    "353",
    "733",
    "2687"
  ],
  "discriminant": "-138121934471648793849592387218589548500103800986006285218689765056222404288",
  "regulator": "1963671448056.6627503530283786458452920277535424219535508229517",
  "points": [
    [
      "2577978443601",
      "-4523790169219049982"
    ],
    [
      "1431726267987",
      "-2187468705449009898"
    ],
    [
      "327853720593",
      "-677438803529294814"
    ],
    [
      "1517017917825",
      "2334868370032644090"
    ],
    [
      "1278942731208307/289",
      "-47222880788985791267818/4913"
    ],
    [
      "78260155090425/169",
      "-1835165858057544065130/2197"
    ],
    [
      "2496275984304",
      "4333727946071531484"
    ],
    [
      "10230307993675/9",
      "-46276998723425538530/27"
    ],
    [
      "1278942731208307/5041",
      "209979956135242228445378/357911"
    ],
    [
      "6742301857",
      "93345240911833898"
    ],
    [
      "2942554657497904/625",
      "-164206860058650562726292/15625"
    ],
    [
      "5750386997425/16",
      "-45744187104995738345/64"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + a x with a = 1292292705051108627666723 (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 21:29:22",
  "updated_at": "2026-10-20 21:29:22"
}