{
  "id": 4915,
  "curve_key": "-315854846313285301728868800:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "6580309298193443786018100",
    "0"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 183.05197497840584,
  "faltings_height": 13.322571659841978,
  "conductor": "3464037636791287415327029772074929316884282208800",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "31",
    "43",
    "47",
    "61",
    "67",
    "73",
    "197",
    "251",
    "271",
    "419"
  ],
  "discriminant": "-18235551256535801615869552264454732404838993000190130333918656019823424000000",
  "regulator": "1858516575653524.6588453746714800210008064729921296841545283612",
  "points": [
    [
      "303696495072100/49",
      "5727879254366890825100/343"
    ],
    [
      "14592574768072900/1369",
      "1813106151673474860636700/50653"
    ],
    [
      "42821855033281/144",
      "2433420388744884939871/1728"
    ],
    [
      "48457216900",
      "564780716219356700"
    ],
    [
      "1032814875625/16",
      "-41724566992766939125/64"
    ],
    [
      "232100502174025/676",
      "-26654074577612151922075/17576"
    ],
    [
      "58740114924100",
      "450625659887237431100"
    ],
    [
      "100120716409156/625",
      "16073495304592853715196/15625"
    ],
    [
      "47429970111364/121",
      "2162454940159220609212/1331"
    ],
    [
      "519858012156025/484",
      "30689444212953441529325/10648"
    ],
    [
      "10414529394025/36",
      "-299909209226704124075/216"
    ],
    [
      "7528246375225/4",
      "34918055273827951475/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4769, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4769.\r\n\r\nThe source commentary attributes the original curve y^2 = x^3 - 1645077324548360946504525*x to Aguirre, Castañeda and Peral, High rank elliptic curves with torsion group Z/(2Z), Mathematics of Computation 73 (2004), 323–331: https://doi.org/10.1090/S0025-5718-03-01547-3.\r\n\r\nApplied the standard degree-2 isogeny with kernel generated by (0,0), sending y^2 = x^3 + A*x to y^2 = x^3 - 4*A*x. Here A = -1645077324548360946504525, giving y^2 = x^3 + 6580309298193443786018100*x. The coordinate map is X = (x^2+A)/x, Y = y*(x^2-A)/x^2.\r\n\r\nTwelve supplied rational points transported through this map and checked exactly on the target curve. Rational torsion C2. Same rank and conductor as the source; conductor 3464037636791287415327029772074929316884282208800. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:48:44",
  "updated_at": "2026-10-20 22:48:44"
}