{
  "id": 3703,
  "curve_key": "365342113526571489260609924941156761:-217358404258308829953077795026127765836850093557095741",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-7611294031803572692929373436274099",
    "251572227150820406941107992934837346654623559944793"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    4
  ],
  "naive_height": 245.65842684219064,
  "faltings_height": 18.356668093335642,
  "conductor": "38689313102431608020253080619974416595190",
  "bad_primes": [
    "2",
    "3",
    "5",
    "19",
    "23",
    "37",
    "113",
    "139",
    "211",
    "281",
    "313",
    "431",
    "547",
    "2029",
    "3919",
    "133319",
    "364943"
  ],
  "discriminant": "879231205253955348350554828866143838724692866639732547959045620293901871503060219460799303495117187500",
  "regulator": "54208061944589.5760061468227627866176097049463495052177352814",
  "points": [
    [
      "2364807755812394003/4",
      "3599008786208349425751663397/8"
    ],
    [
      "-693010585961443059943727/7112889",
      "156742416214813186243785276861903167/18970074963"
    ],
    [
      "-41499170854430919948/6241",
      "8566530759101273997186980175841/493039"
    ],
    [
      "17584056715193141387/2209",
      "1436699076112744762504647218773/103823"
    ],
    [
      "812788623068776491542/18769",
      "4582719319980408746759670624583/2571353"
    ],
    [
      "5145492978757711849337/5041",
      "367790134665995419637380971116974/357911"
    ],
    [
      "166610169206108633758497/5812921",
      "105776448848103657748393686284294054/14014952531"
    ],
    [
      "7631006540194929675791588/445336609",
      "105567426295238227787227957900493609843/9397938459727"
    ],
    [
      "15897188583598396723988687/218418841",
      "29436552935682957539932653090768275726/3228012051139"
    ],
    [
      "2713542141353455416534011557/15438311001",
      "126426800804935009012385897687464852076534/1918225580185251"
    ],
    [
      "11495174120583970392472298327/51651198361",
      "1149003424635537492826169665566348838906331/11738716200306109"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 5941/17480 of the Elkies-Klagsbrun Z/4 fibration E1: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = (8t-1)(32t+7), c = 8(t+1)(15t-8)(31t-7) (arXiv:2003.00077, eq. (5)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-30 01:46:20",
  "updated_at": "2026-09-30 01:46:20"
}