{
  "id": 741,
  "curve_key": "1186520650215772875800162759623717973361:-40946431280392935040349286491053242403676947838633606793609",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-24719180212828601579170057492160791112",
    "47391702870825156302880358121555810584233426223310576011"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 269.9192299178842,
  "faltings_height": 20.28959176978458,
  "conductor": "285127989577366463602132412866032046495440428541331418487010272748599472215982187571742566090",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "71",
    "167",
    "331",
    "6069359856253097435968757534882932707863997605785760719997398795931953981426425791"
  ],
  "discriminant": "-3581817381584736626539463005040817283661181362510750827824228493835005777574473248347475247679189446389350400000",
  "regulator": "5526246359474649847727468.47853535152504266359101957419652333514191673253699445774117",
  "points": [
    [
      "-22575665299102729301/4",
      "-21353487918194478103500509003/8"
    ],
    [
      "-1530719795708822612261/289",
      "-26787410737448509035988635381053/4913"
    ],
    [
      "-4832733281848505399",
      "-7347306928417846304904593131"
    ],
    [
      "-4577561193529737779",
      "-8039075901141629108583061351"
    ],
    [
      "2787058054379729023549/21904",
      "-21564253737022941925286348350825597/3241792"
    ],
    [
      "1064553192973284061",
      "-4720513804264481972715394711"
    ],
    [
      "2755570362973209101",
      "-446957774487481156733454631"
    ],
    [
      "1236649940928174013669/441",
      "-3275773587788014820368488006491/9261"
    ],
    [
      "2815341335213744461",
      "-337019073743250492215490151"
    ],
    [
      "2854297658463146845",
      "-299684601584575040329349143"
    ],
    [
      "2863314574029295195",
      "-296647735793977492589508973"
    ],
    [
      "3112304753238993781",
      "-777969655096012041637388191"
    ],
    [
      "3840255605086087969",
      "-3016313050844787695476354351"
    ],
    [
      "3940012470857440381",
      "-3340866557604030454744700791"
    ],
    [
      "15155610266640817741",
      "-56159485354659128123567008231"
    ],
    [
      "26392308830609903221",
      "-133336652277112992703816947871"
    ],
    [
      "44302531378709882381",
      "-293096367644938946602706154791"
    ],
    [
      "48873318470260445851",
      "-339967871052194716215454414381"
    ],
    [
      "53359276904856718381",
      "-388141199433402919404101786791"
    ],
    [
      "187641881641776082381",
      "-2569471019355850395692985554791"
    ],
    [
      "237094338194774458361",
      "-3649951039343480925580881020411"
    ],
    [
      "524310693823647927931",
      "-12005040185089405474501401544141"
    ],
    [
      "955087478061963815161",
      "-29516091914473020230414210711551"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization T=-61/126 of the family identified by wgxli in the commentary to curve #302. The points were obtained by specializing reconstructed generic sections and running minimized quartic searches. The 23 listed points are certified independent by exact quadratic-character certificates.",
  "created_at": "2026-09-16 18:14:06",
  "updated_at": "2026-09-16 18:14:06"
}