{
  "id": 407,
  "curve_key": "178077654284665204561131241:-2394989620945844358227293333643729836789",
  "ainvs": [
    "1",
    "0",
    "1",
    "-3709951130930525095023568",
    "2771978727946269955724382333144546458"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "naive_height": 181.34839504797392,
  "faltings_height": 12.966584500601362,
  "conductor": "417915012125990192528679544512198522920598025470860459357489652330",
  "bad_primes": [
    "2",
    "3",
    "5",
    "5711",
    "7290821",
    "334563162888224059184705111206367940720505405735115281"
  ],
  "discriminant": "-51411382397974155997137496716460022041538318345893415134584180167571187500",
  "regulator": "32782880949544867900.965466547617252390471883374763399879940054415135280760",
  "points": [
    [
      "2130601975627",
      "2130572130898993337"
    ],
    [
      "25751724149899231/12769",
      "2696525099524257749295235/1442897"
    ],
    [
      "14606543505187554259/654481",
      "55622719438366410944021466115/529475129"
    ],
    [
      "30109621143837/121",
      "-1817292188647547371933/1331"
    ],
    [
      "-92678458986528884/70225",
      "43122760131099770560951166/18609625"
    ],
    [
      "-47360087420559161/63001",
      "35837418091206943031772985/15813251"
    ],
    [
      "7707330871611488179/7447441",
      "4112717069346587762867669635/20324066489"
    ],
    [
      "702781138515934/961",
      "19984098585996791370065/29791"
    ],
    [
      "2744907957921668101/2362369",
      "628639679469781529381272385/3630961153"
    ],
    [
      "623271490551691/529",
      "2322646692772128950815/12167"
    ],
    [
      "4211082445460553484/829921",
      "-8093208125551926636000039125/756058031"
    ],
    [
      "8118426680105016394/22201",
      "-23131394115574413530320203665/3307949"
    ],
    [
      "4359600934191271/25",
      "-287835092950230505646471/125"
    ],
    [
      "31688813019094159/32041",
      "-1519514179290520924897145/5735339"
    ],
    [
      "30942968920004368964884/1077874561",
      "-5431112771346199973574437432939885/35387699712191"
    ],
    [
      "22308177456532574119/44903401",
      "-308545565525824024705212447185/300897690101"
    ],
    [
      "130200220826670817/10816",
      "46412985402759744291977683/1124864"
    ],
    [
      "18357118322078602/27889",
      "-3653035558070951451401651/4657463"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "commentary": "Rank-18 curve from Mestre's quartic construction, specialized at T = 235/3. 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.",
  "created_at": "2026-08-28 20:29:12",
  "updated_at": "2026-08-28 20:29:12"
}