{
  "id": 5250,
  "curve_key": "-193636471976953629768144:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "4034093166186533953503",
    "0"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 160.8608084948559,
  "faltings_height": 11.473307786212814,
  "conductor": "10627858072472094204174121166893361218593312",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "23",
    "31",
    "47",
    "53",
    "67",
    "83",
    "199",
    "251",
    "389"
  ],
  "discriminant": "-4201629422893286305152814322400756714397872868867397507408127649728",
  "regulator": "41624158494.12960260592823494872155269337593272704107183244",
  "points": [
    [
      "1916259513",
      "2781619313956644"
    ],
    [
      "4593622033",
      "4316020266301744"
    ],
    [
      "7486596348",
      "5533646567958894"
    ],
    [
      "30295150396",
      "12248192976926018"
    ],
    [
      "138613224633",
      "56766551110401756"
    ],
    [
      "151603576047",
      "63999887594127408"
    ],
    [
      "993247230976",
      "991909792540514848"
    ],
    [
      "520244904111/20449",
      "936804545179121315208/2924207"
    ],
    [
      "512427725025216/7921",
      "16255890186395368701192/704969"
    ],
    [
      "2594165357940156/37249",
      "178824344135504418729378/7189057"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5249: https://elliptic-rank.icarm.cloud/curve/5249. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (5,14,19,21), 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. Ten rational points checked exactly; PARI/GP returned rank bounds [10,10]. Rational torsion C2.",
  "created_at": "2026-10-21 11:09:17",
  "updated_at": "2026-10-21 11:09:17"
}