{
  "id": 4956,
  "curve_key": "-542885589863293943590456169664:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "11310116455485290491467836868",
    "0"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 205.40008832551558,
  "faltings_height": 15.18491443876779,
  "conductor": "28426385385919811326943632130923115672884025713568899872",
  "bad_primes": [
    "2",
    "3",
    "11",
    "37",
    "41",
    "73",
    "151",
    "269",
    "509",
    "673",
    "1193",
    "2969",
    "5233"
  ],
  "discriminant": "-92593649987498372524976943202870015922373495692111323726565619549584713834652759298048",
  "regulator": "886182979214302081.1109252823191103716555703841952564599063790351",
  "points": [
    [
      "54775811295659584/180625",
      "4495806112627929636853621552/76765625"
    ],
    [
      "699203681856",
      "88929280322281525968"
    ],
    [
      "7345633940089/4",
      "1153115763064220452499/8"
    ],
    [
      "87181996057997940961/1285956",
      "1514344486321622067469230323953/1458274104"
    ],
    [
      "162028327072075776/2209",
      "114874118852808851287360128/103823"
    ],
    [
      "7695354356773229584/81225",
      "32092413120677675072578483448/23149125"
    ],
    [
      "997916896701123800976/8720209",
      "43035061545587752613579554491672/25750777177"
    ],
    [
      "2930721635961723136/24025",
      "6656177769911942390198995616/3723875"
    ],
    [
      "19884452957915536/81",
      "3055762148645924962375528/729"
    ],
    [
      "272435343420305664/961",
      "151875115379530685420122656/29791"
    ],
    [
      "44313591316015524315024/116488849",
      "9686038889173652989958061750408984/1257264147257"
    ],
    [
      "1213887473283818754304/4133089",
      "44980207193550907025131442514976/8402569937"
    ],
    [
      "130244280022588176/49",
      "47041950898148877576974088/343"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #52, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/52.\r\n\r\nThe source model is y^2 = x^3 - 2827529113871322622866959217*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 = -2827529113871322622866959217. The resulting model is Y^2 = X^3 + 11310116455485290491467836868*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 28426385385919811326943632130923115672884025713568899872. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:47:37",
  "updated_at": "2026-10-20 23:47:37"
}