{
  "id": 312,
  "curve_key": "315264939877372775500086784223505252652923586495425:-5492490078933343561132867399029248283339362874888755114066682669387927710625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-6568019580778599489585141337989692763602574718655",
    "6357048702469147640200079650140599226292653501480652916481851397620447847"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 348.8324934840207,
  "faltings_height": 26.962675275157576,
  "conductor": "565363502863493379565569563649307108299188776386222378070363275106421667133549554450",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "47",
    "61",
    "71",
    "79",
    "83",
    "101",
    "127",
    "137",
    "229",
    "241",
    "293",
    "311",
    "523",
    "541",
    "827",
    "1009",
    "1753",
    "3331",
    "4091",
    "6637",
    "9007",
    "16069",
    "44263",
    "52609",
    "67157"
  ],
  "discriminant": "675555591393920126210578335859174012733377876129576927329773074052725622143925022750267503150613919256894560960666950209537112482403220443264000000",
  "regulator": "55334661388047328635264.233241137894046053441742156612656109565455169",
  "points": [
    [
      "46664353179227656746344209195170267/5869551769",
      "-9609414434353093913425768111368704314373409144654338/449683969678397"
    ],
    [
      "20500362356964924142848252139122731/1440733849",
      "2890519800749380699697383530571870546009094699988270/54685934706493"
    ],
    [
      "427407679394957380896328721938730067509/240947043855961",
      "-2006826744292694090548290082282236945466283191949070963840/3740093018895795087709"
    ],
    [
      "103167544390400490835793902896668795/62785826041",
      "-554359388049341210240512232520526671728133838978014/15732307216919411"
    ],
    [
      "134729047327530661756060101/25",
      "-1411330887440267498472117124542946898064/125"
    ],
    [
      "717049180243690501327959841006625/354907921",
      "-7723018542827921882484225749198651619683288538396/6686110323719"
    ],
    [
      "3259714524420718295605994459353331/1552911649",
      "-82539375370618395063776110058719841807163463349430/61195589352143"
    ],
    [
      "1693650329908056916337234543972315/87179569",
      "-69121783083240021677521702496053712441134400754162/813995635753"
    ],
    [
      "536301036363160960997997589169635/75325041",
      "-11703903112195500857742495776305395631020516683398/653746030839"
    ],
    [
      "6538582364882675844199175387060159/1771561",
      "528719457855062509908391094465081265327115697049090/2357947691"
    ],
    [
      "640676361896207555519981883276618853401/101299655541529",
      "15046710442381457969025156385343767062708474199448217868380/1019558038003681457917"
    ],
    [
      "19021380651749437931176718556811035/10293928681",
      "-760212660155743957404916573496430843743000260111566/1044411710045579"
    ],
    [
      "231690727121059545502326343077/61009",
      "-90646366578917143905881190906667010579665192/15069223"
    ],
    [
      "32672882199157031838907171/9",
      "148764467232755722042553420072889834730/27"
    ],
    [
      "4428458137325117467968668572701367/2582977329",
      "-48397502483322969510165969342065192368038716287990/131274656791767"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": null,
  "created_at": "2026-08-24 00:23:57",
  "updated_at": "2026-08-24 00:23:57"
}