{
  "id": 4955,
  "curve_key": "17354812277926925025916480320:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-361558589123477604706593340",
    "0"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 195.07100203048688,
  "faltings_height": 14.324157247515398,
  "conductor": "261449226737919396153756025756944483500777736264711200",
  "bad_primes": [
    "2",
    "5",
    "7",
    "23",
    "43",
    "83",
    "97",
    "101",
    "269",
    "461",
    "503",
    "4013",
    "12829"
  ],
  "discriminant": "3024934833497162686050347554121116315071052598236867512524693823772358750189056000",
  "regulator": "1136695045238009246.448271695484372499814115408872005847445554431",
  "points": [
    [
      "517090301540167744/625",
      "-371736203284930474154448528/15625"
    ],
    [
      "5632368470353243629481/43322724",
      "-418158783519914666023158488474699/285150169368"
    ],
    [
      "26142446318371319281216/402443721",
      "-4041733244583265029872292304420784/8073423486981"
    ],
    [
      "276759024677776/9",
      "-3618463631608368614744/27"
    ],
    [
      "94435297650213372304/4363921",
      "-438117217405978951419459383448/9116230969"
    ],
    [
      "15744425213415940490089/807810084",
      "-433744963449904449151608213968597/22959578207448"
    ],
    [
      "43256758040939169392656/2236817025",
      "-1639541464778178308226289135856696/105790261197375"
    ],
    [
      "72195162476327869801/3794704",
      "-20423928271305007865760534219/7392083392"
    ],
    [
      "16215812343719135150656/811053441",
      "638189070880236910111547605890224/23097990946239"
    ],
    [
      "37920059908806019089721/1415264400",
      "5202404789782769328664553170895981/53242246728000"
    ],
    [
      "5151777523981456/169",
      "289020165134914673049624/2197"
    ],
    [
      "1694955295874542144/44521",
      "1911726562888575410902031568/9393931"
    ],
    [
      "13523713699102130176/269361",
      "46028203797814171033070738944/139798359"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #51, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/51.\r\n\r\nThe source model is y^2 = x^3 + 90389647280869401176648335*x. Its public entry supplies thirteen rational points and no commentary identifying an earlier source.\r\n\r\nApplied the degree-2 isogeny X = (x^2 + A)/x, Y = y*(x^2 - A)/x^2 with A = 90389647280869401176648335. The resulting model is Y^2 = X^3 - 361558589123477604706593340*X.\r\n\r\nThirteen supplied rational points transported through this map and checked exactly on the target curve. Rational torsion Z/2Z. Same rank and conductor as the source; conductor 261449226737919396153756025756944483500777736264711200. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:46:25",
  "updated_at": "2026-10-20 23:46:25"
}