{
  "id": 5351,
  "curve_key": "347334604848:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-7236137601",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 79.7206632941271,
  "faltings_height": 4.711629019485415,
  "conductor": "186174888464377014048",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "41",
    "71",
    "211"
  ],
  "discriminant": "24249367994023073887071084339264",
  "regulator": "14101074.56582729467066805068027326735225795104059372",
  "points": [
    [
      "5221225",
      "-11928915620"
    ],
    [
      "249001",
      "-116775980"
    ],
    [
      "990025/9",
      "-624573440/27"
    ],
    [
      "94249",
      "12458060"
    ],
    [
      "22762441/225",
      "58781983364/3375"
    ],
    [
      "1555009/16",
      "937825055/64"
    ],
    [
      "10426441/16",
      "33378899525/64"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (9,13,25,30), followed by a rational 2-isogeny and fourth-power reduction. Reference: \"High rank elliptic curves with torsion group Z/(2Z)\", Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3. Seven rational points transported through the isogeny and checked exactly. PARI/GP returned rank bounds [7,7] for the source curve; rank ≥7 transfers through the rational isogeny. Rational torsion C2.",
  "created_at": "2026-10-21 15:38:55",
  "updated_at": "2026-10-21 15:38:55"
}