{
  "id": 1378,
  "curve_key": "55137693380355095108441260425985160998019462401:11599352020102159990457503120638109845535638003427875463765146718646399",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1148701945424064481425859592208024187458738800",
    "-13425175949192314803770353966641412474743403547822354677669726560000"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    6,
    2
  ],
  "naive_height": 322.87848827218596,
  "faltings_height": 24.882384463652432,
  "conductor": "358210529915244759591648810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "29",
    "139",
    "593",
    "859",
    "11503",
    "1563539"
  ],
  "discriminant": "19145098994861964429545895795064363715838657765757988550449924211657419900402361867585237450291573423636384944073772803768309427776000000",
  "regulator": "2561826934.968044209846524272240591056019182854",
  "points": [
    [
      "3459372024841640952411837154405815117432862646708103372784/22320631498402761986540384963272225",
      "-198166875500239066433596644069566652861371257081638422683928762045035015959900308373872/3334722626977077116979387646264686004463160148776625"
    ],
    [
      "-115849515182759448989118228092918740276199661207808871474957819631768043559683817420464841010324095039078104454477848823277387848275856/7177727205270570057746402633715884567999175196751121949519151718858920049446788130313934713665091215319555172249",
      "580244574731810460967718608054886189082981303485571028617212680759227438612191302417641875585308158725101443369371483065893355232243736357819347836117048477008680905980799173081404770831785279927572144/608107588495791235839739509161637523196274644747714670952516785938680757464933092288979154458488981008095930013423934142416609367270860988093742568337928915425680490307"
    ],
    [
      "399593379739314574336578547019108773488466809009931469065232613219636499493968973439911749726509784763544841988240016243347647684217175179663219448821344/8056177872254582676980706294577184259997234695478874763716904136510115910356477716889815941369550824869725733776299860412067352025",
      "-5195632564736435155903361660859355514240271363618206505869782031129352137039043003915589321502375308511303533638028863092326206650098994264543163941747663382581791732016221431078692267727738970496168148045154251813970567966626832/723092021562655744601947615885004547901859369927552335642016188868564374809885164677688818157230304157648672821651940428520588960478405831853311398574120882027536560006238230194911466697766283875"
    ],
    [
      "-41136470860494839377794709142319440747656047486842241379752276249994046871120406631653433087635938608941883821145614241276160384794406493856861738482833480029478648284716112606322194883881112672249500/2819113211622475213320884009337927744657006130928310486369538617448777835685135282393420895021956488506885600928880914483821638175419358861189230166553956997493804986052917113921",
      "71730912758312799723931275798837728830101076785547064756182350162149685348656285854428920497270283177306765831736570543133114700641239310895260347516362681020646491721152171496891669933677038486700897045569949901313887119089789437064670549380873363012430497599084339999480979215845900292452727367200/149681723548709951482699628507792218991645927590138611435744784788839148481660143172914988986614976027381840157934679904444575599240053904942476446632901698148864455483478245069016921675733240367982362214552494711705104603084059648991649094764812076430859227844144031"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Obtained from ICARM curve #1105, a rank-at-least-4 curve with torsion \\(\\mathbf Z/12\\mathbf Z\\), found by Tom Fisher (2008). Quotienting by its unique rational point of order 2 gives a 2-isogenous curve whose global minimal model has ainvs \\([1,0,0,-1148701945424064481425859592208024187458738800,-13425175949192314803770353966641412474743403547822354677669726560000]\\), torsion \\(\\mathbf Z/2\\mathbf Z\\times\\mathbf Z/6\\mathbf Z\\), and conductor \\(358210529915244759591648810\\). The four independent source points were mapped through the isogeny, yielding four independent points on the quotient. The isogeny, minimal model, conductor, torsion and image points were verified in Magma.",
  "created_at": "2026-09-24 19:00:19",
  "updated_at": "2026-09-24 19:00:19"
}