{
  "id": 3705,
  "curve_key": "3574813592286826462606443176749299845028718561:-213708393714671743545048904470676085867121265187798793755514373039441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-74475283172642217970967566182277080104764970",
    "247347677910499703177133729456351453272485365188696377089984756900"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    4
  ],
  "naive_height": 314.67072665250276,
  "faltings_height": 23.92762097911625,
  "conductor": "15662834656502411939691591195371771384959399565490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23",
    "29",
    "37",
    "43",
    "53",
    "59",
    "83",
    "107",
    "109",
    "127",
    "157",
    "269",
    "347",
    "607",
    "3181",
    "1307863",
    "23637023"
  ],
  "discriminant": "7123832361906247191371462610390964156376565481484328767269317132582264854770161061912366467847004494651785981833610000000000000000",
  "regulator": "23535455614929.693934462849057192885911045488528206208036582120",
  "points": [
    [
      "-9662873523069354350924",
      "254478979291982856719720850726022"
    ],
    [
      "-5306102752051519906124",
      "702231665193734787878365835306182"
    ],
    [
      "-4500003457382048915291454930860/483956001",
      "3924978233451101789147565951534611492168382170/10646548065999"
    ],
    [
      "-20722315561156134184974260/17161",
      "1302181647400992693483240433126869501530/2248091"
    ],
    [
      "1883051960445228836428060/169",
      "1966104478095500013521664633234158710/2197"
    ],
    [
      "28295446937927571442055860/5329",
      "15571803272302098552738507543300041110/389017"
    ],
    [
      "74297587920633603034388740/361",
      "639861694273216760305089614685182931970/6859"
    ],
    [
      "317364771080981374324062307/64516",
      "84094696430311301507549844855870297929/16387064"
    ],
    [
      "1276529578273313214373850365/309136",
      "17380247482794805895225233588331109520405/171879616"
    ],
    [
      "1934778697896993418050603398740/369831361",
      "214448296867995806651366992897018674198725530/7112226903391"
    ],
    [
      "24951713764973725380369654005140/5059334641",
      "796740332664876848228377229270651371260550070/359865413679689"
    ],
    [
      "74014217019024291840717546212054172531000750256456139037940/10591590664163077422384337039058024241",
      "-8998902468908999721087975365309704457055047897471497250108461482321300429462183114631370/34470039589181745927702152856328997986725083560565873961"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -30706/18375 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 01:46:42",
  "updated_at": "2026-09-30 01:46:42"
}