{
  "id": 4884,
  "curve_key": "-524578075037508695472:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "10928709896614764489",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 143.1273778403283,
  "faltings_height": 9.995521898335515,
  "conductor": "699437433383344927296",
  "bad_primes": [
    "2",
    "3",
    "17",
    "31",
    "449",
    "4657"
  ],
  "discriminant": "-83538498902829944623441924685266184259595132988614160778816",
  "regulator": "171548757.28535283125443040529488388664191257649192",
  "points": [
    [
      "97939580209/64",
      "72963135958762025/512"
    ],
    [
      "230084268241/64",
      "149932883227172455/512"
    ],
    [
      "33751579971321/484",
      "196303761149335638165/10648"
    ],
    [
      "157943614623844/42849",
      "2666329018294616941490/8869743"
    ],
    [
      "31992921511647216481/10347772176",
      "264923750822104715098353217775/1052616776831424"
    ],
    [
      "1003915610457358114485841/16248564188660736",
      "53829937888198920790476022975412110375/2071202137335340850774016"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4721, submitted by David Renshaw and sourced to Watkins et al.'s electronic data PTS.r6r7: http://magma.maths.usyd.edu.au/~watkins/PTS.r6r7, accompanying Section 15 of Ranks of quadratic twists of elliptic curves (2014): https://doi.org/10.5802/pmb.9. Six rational points transported through the isogeny and checked exactly. Rational torsion C2. Same rank and conductor as the source. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:28:32",
  "updated_at": "2026-10-20 22:28:32"
}