{
  "id": 5083,
  "curve_key": "-66429595108800:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "1383949898100",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 95.48149134774556,
  "faltings_height": 6.025031357286954,
  "conductor": "17025042848453336743200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "31",
    "37",
    "757"
  ],
  "discriminant": "-169645005469908929724167706249024000000",
  "regulator": "1386192.402946065675091624234160519044966217900701724",
  "points": [
    [
      "5670",
      "88584300"
    ],
    [
      "206116",
      "542227636"
    ],
    [
      "878416",
      "1376038664"
    ],
    [
      "911680",
      "1421081200"
    ],
    [
      "1372525",
      "2117806075"
    ],
    [
      "3513664",
      "6945635312"
    ],
    [
      "9490030/9",
      "43800802100/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5082: https://elliptic-rank.icarm.cloud/curve/5082. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (12,38,42,52), 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. Points transported by the rational 2-isogeny and reduced with PARI/GP. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C2.",
  "created_at": "2026-10-21 02:22:10",
  "updated_at": "2026-10-21 02:22:10"
}