{
  "id": 4988,
  "curve_key": "116142155566397083200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-2419628240966605900",
    "0"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 138.60403978120004,
  "faltings_height": 9.618577060074827,
  "conductor": "468368065958652117289244717273184800",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "19",
    "23",
    "47",
    "73",
    "229",
    "613",
    "1493"
  ],
  "discriminant": "906621279648371737004856847043431749663075471576256000000",
  "regulator": "1057130905635.42882907245550715514854717522180497359861784009",
  "points": [
    [
      "-1300645170",
      "30770199045300"
    ],
    [
      "-1211146650",
      "33969433808100"
    ],
    [
      "24163875670",
      "3748419338819100"
    ],
    [
      "-128172384979100/120409",
      "1546196246464613366700/41781923"
    ],
    [
      "-6939299057130/17161",
      "67901795768726181900/2248091"
    ],
    [
      "-2284181011530/72361",
      "170080568064360059700/19465109"
    ],
    [
      "-379917716570/14641",
      "14035548817692719100/1771561"
    ],
    [
      "-5134288775/64",
      "7123871883911475/512"
    ],
    [
      "6264204545/4",
      "57413121892575/8"
    ],
    [
      "42746199430/9",
      "8350427448441100/27"
    ],
    [
      "1739174135658470/1062961",
      "22489792679397797634300/1095912791"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of David Renshaw's curve #4986: https://elliptic-rank.icarm.cloud/curve/4986. His source is the Aguirre–Castaneda–Peral parametrization at tuple (89,102,168,214), from \"High rank elliptic curves with torsion group Z/(2Z)\", Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3. Points transported by the rational 2-isogeny and reduced with PARI/GP. Eleven rational points checked exactly; PARI/GP returned rank bounds [11,11]. Rational torsion C2.",
  "created_at": "2026-10-21 01:17:03",
  "updated_at": "2026-10-21 01:17:03"
}