{
  "id": 4920,
  "curve_key": "-232176076018643704999202083270800:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "4837001583721743854150043401475",
    "0"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 223.5751464659647,
  "faltings_height": 16.69950261713855,
  "conductor": "29947627930786122521100129658764695285207276277281520681184800",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "41",
    "61",
    "89",
    "101",
    "643",
    "1361",
    "3491",
    "6091",
    "87049"
  ],
  "discriminant": "-7242836186496100273720517166994397525633436690183738858399022413901040873369236321253379000000",
  "regulator": "7717123732098616060.793635884807856566151225963094948360605584594",
  "points": [
    [
      "723532334796347521",
      "615444540179803540505007106"
    ],
    [
      "30161693346058725025/9216",
      "-199575122653204358488857069425/884736"
    ],
    [
      "47003939816091544225/1521",
      "323071340376439125134183927350/59319"
    ],
    [
      "1743863331494750193025/133956",
      "-73854942262788893384042033343175/49027896"
    ],
    [
      "637104342661937846809/10816",
      "-16092308821735297693709471163523/1124864"
    ],
    [
      "64484906527276225/81",
      "48110423901732271379731850/729"
    ],
    [
      "12501517469734225",
      "-1419262576161730387327850"
    ],
    [
      "1945047604405633225/131044",
      "401957617431982694530200333475/47437928"
    ],
    [
      "49263183621520968583969/150822961",
      "74431065631631097247011992992176022/1852256784041"
    ],
    [
      "4299239441320355379961/714025",
      "-300111625378230279725991037174834/603351125"
    ],
    [
      "4075898141679535155625/23454649",
      "-3303544868133753276014850674719250/113590865107"
    ],
    [
      "207182880369703992601/21904",
      "3061712974109979622067116295549/3241792"
    ],
    [
      "211362237274132266522216025/229567473424",
      "7957511687308608836144479454192568520925/109993122676587968"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4776, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4776.\r\n\r\nThe source commentary attributes the original curve y^2 = x^3 - 19348006334886975416600173605900*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), followed by the rational change of coordinates dividing x by 4 and y by 8. With A = -19348006334886975416600173605900, the combined map is X = (x^2+A)/(4*x), Y = y*(x^2-A)/(8*x^2), giving y^2 = x^3 + 4837001583721743854150043401475*x.\r\n\r\nThirteen 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 29947627930786122521100129658764695285207276277281520681184800. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:53:37",
  "updated_at": "2026-10-20 22:53:37"
}