curve #546

y² = x³ + x² − 18246910332422325808743943527578574466277017300x + 944782400514670765250929378486561230321389981851401513256985799260000

a-invariants: [0, 1, 0, -18246910332422325808743943527578574466277017300, 944782400514670765250929378486561230321389981851401513256985799260000]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 10887498191560432338721638471418532230896369787408837398174099584244909545295388568853954802838927940102360
discriminant (Δ): 3210300557981597596545080841479651055189645285449925578536562377164067025082815464456871511022476875605526397510778845140613758038500000000
Faltings height: 25.4260
naive height: 331.1746
primes of bad reduction: 2, 3, 5, 7, 13, 19, 37, 53, 67, 113, 151, 179, 5077, 7192464743209503570751709, 13826312523583685680219862970876888333926988840779038753889
regulator: 2481570031922119244993690793.384213576719524114253454107190112141837208351220968925871699
submitted by: 7fff-zip
submitted at: 2026-09-03 04:23:35 UTC
last updated: 2026-09-03 04:23:35 UTC

Witness: 25 independent points log in to add more points →

(-151996504274403450836830, -14376483402125277736980941894898030)
(-64322874810107892219400, -43038873062955245466383642880208200)
(2098716618209409538443938, 3034251295094907207048617684037606546)
(-19215996053205503798595508/169, -86481833669115589716949076355324353448/2197)
(569013127529775075426850/9, 178823591898004154138456017944745750/27)
(5041067312819990865650, 29204907168034697835431146885853250)
(100209810628475061475250, -11071156479249648420088920261259650)
(-620187050747870532482275/4, 54646698852873392640876241938658125/8)
(39679234140636588684268280, -249943823050218738457681269777254617080)
(2498131440531623634926525/4, 3862787319686609698778548910887110525/8)
(508399750940325439185650, -350819465412617387227860025815389250)
(228393045137490434821610, 93225902455957333900547636541728490)
(8728733264811702150867965/4, -25740263048358142522171091080776775005/8)
(73327690794962710081775, -1028565076998141271335010558533750)
(-85179709869064209453850, 43370732943241552255879597070846250)
(70957001296180260122150, -2701385707666715836184025998822250)
(83809647344318035001150, -2049150926572184039525340790938750)
(193044615591536443967915, 67943788684354618807178943385286940)
(1363961806285028285155780600/18769, 4099796861291775385499279655177816135000/2571353)
(152151689072807381527429734236300/737881, 1876787376780821524772877347157881252901605064600/633839779)
(30633332659603596619239567350/418609, -317903599035863422709744296533162882777750/270840023)
(39704041681064766721692980600/552049, -866860485477699542074829451510342597261000/410172407)
(17730930571718176774783485163490/208253761, -8714573468789251499502167742307965785066260590/3005310024991)
(132513802373676687578077850/169, -1504137915813675325393515670992043919250/2197)
(43125863335660425161535950/289, 193101360963282051784644556820690599950/4913)

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