{
  "id": 405,
  "curve_key": "794346871955316577232569857:-23188999639329388098384189954926929733889",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-16548893165735762025678539",
    "26839119952931669744569431573523699419"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "naive_height": 185.88899327903312,
  "faltings_height": 13.411910370979298,
  "conductor": "240304052236271865792163224043927979467874502821068908703531542",
  "bad_primes": [
    "2",
    "3",
    "13",
    "41",
    "43",
    "47",
    "11953",
    "12251",
    "74781881959",
    "1131749254105640328087296214832246279"
  ],
  "discriminant": "-21126847178478909706119014513238013838343083475096497271069314604074275454976",
  "regulator": "4640709170520558901.4172077288912774504840462322039265644301731391197884209",
  "points": [
    [
      "-3306824380777",
      "6738175697315251290"
    ],
    [
      "30189185258932871/12769",
      "-1390580896453340819530722/1442897"
    ],
    [
      "4369528301117614763/6806881",
      "72095243229002689456392010794/17759152529"
    ],
    [
      "1047908035222739/484",
      "-11460156637937551294845/10648"
    ],
    [
      "10912976686778979919/1347921",
      "-32206576579933461969079244854/1564936281"
    ],
    [
      "792737529466027007/63001",
      "672921097931015116803137130/15813251"
    ],
    [
      "48157403470146683627/15124321",
      "-149123370299841519846785247702/58818484369"
    ],
    [
      "3407404363506107/961",
      "106324670147184170633670/29791"
    ],
    [
      "5779643108996866883/1885129",
      "-5741500542469560803558747406/2588282117"
    ],
    [
      "-2493593895740149/529",
      "3992508993373073837238/12167"
    ],
    [
      "423731527338700710563/20241001",
      "-8569129758536490184358041766226/91064263499"
    ],
    [
      "106206734690790299/841",
      "-34594380527848246207318926/24389"
    ],
    [
      "3842127816779",
      "4469163678560637066"
    ],
    [
      "2042955394907",
      "1247830848076410762"
    ],
    [
      "5499749719694097251/2468041",
      "3929861750163129309397079118/3877292411"
    ],
    [
      "36951547614887849/25",
      "-7103089895787010745805378/125"
    ],
    [
      "7063245280319323154867/205664281",
      "589635975504701258328782671968930/2949431453821"
    ],
    [
      "7293197365467156371/546121",
      "-18876049844717598811972197090/403583419"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "commentary": "Rank-18 curve from Mestre's quartic construction, specialized at T = 2383/4. The sextuple is [0, 113, 550, 753, 868, 1058], the canonical primitive representative from u = -3, v = -1/2 in the Mestre-Fermigier family, whose generic member has rank 12. Rank is exactly 18.",
  "created_at": "2026-08-28 20:28:59",
  "updated_at": "2026-08-28 20:28:59"
}