{
  "id": 5237,
  "curve_key": "104273625456:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-2172367197",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 76.11085288508798,
  "faltings_height": 4.410811485398822,
  "conductor": "16779303959472486432",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "59",
    "61",
    "67"
  ],
  "discriminant": "656114571180904445080278679872",
  "regulator": "26578.18355823189941634549594659745069911131874740839",
  "points": [
    [
      "-25311",
      "6226506"
    ],
    [
      "-9581",
      "4464746"
    ],
    [
      "48321",
      "2802618"
    ],
    [
      "343308",
      "199290294"
    ],
    [
      "-327509/9",
      "149999122/27"
    ],
    [
      "-154167/4",
      "41162589/8"
    ],
    [
      "-118767/4",
      "49525839/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (10,13,18,19), reduced by rational fourth-power scaling. Reference: “High rank elliptic curves with torsion group Z/(2Z),” Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3. Selected in a bounded tuple search following the parametrization search described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C2.",
  "created_at": "2026-10-21 10:50:24",
  "updated_at": "2026-10-21 10:50:24"
}