curve #1875

y² + xy = x³ − 1775696843283544739944327907722249335766575x + 909202126879189160581582055495280775299970420584394073368396857

a-invariants: [1, 0, 0, -1775696843283544739944327907722249335766575, 909202126879189160581582055495280775299970420584394073368396857]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 25416567991290065057789224363709677154888513243554834027231104845904999090778871673901699470
discriminant (Δ): 1220544700652714420179358336475494467597198033256509599763523147541917431234570468738867258917562644026472274986327932928000000
Faltings height: 23.0818
naive height: 303.4619
primes of bad reduction: 2, 3, 5, 7, 17, 19, 23, 29, 53, 71, 139, 310049, 494870838528934750897067155684583970359408948781221375605432471166667577
regulator: 4589235255617488642801708.4877822428533495201259961332998473803725472506944637088549104
submitted by: Ritik Jain
submitted at: 2026-09-25 17:25:30 UTC
last updated: 2026-09-25 17:25:30 UTC

Witness: 24 independent points log in to add more points →

(153554855174556883250046/49, 55434446485058769180410446062845739/343)
(693309442745480879364, 3369469214303466517629508014303)
(153461377673440508942118/529, -248900986855422248126823597622699605/12167)
(74284006467917273015454, 20242939285964215596418859124781773)
(55268917786918286064102954500904276584647776828858481893366/32267529276665202878884929971778368929, 9858499163872935534301203915767942224516524041612207675699743110214105982138619751652109/183294135174122960462390456993098791399005362821400258033)
(117417046855160476510714854/160801, 89462825930629483624809471034289876973/64481201)
(656456919790840578375894/961, -115289322692023919777526481421453757/29791)
(-1030955118713373291546, -40547456155046838227293252036227)
(17905843385322456683094/25, 274130295208936192857564682883337/125)
(653688870946180658054, -5270302792513564722580730866627)
(56115853208060351724054, -13289449495225146569891020097093427)
(1839638650547131074882100806/543169, 73537549508186146461100148744407557400029/400315553)
(604791831309496243193161614/1207801, -16016593593541672040408783877496228016553/1327373299)
(146294559491867475382/9, -801105313750931938991221226059153/27)
(66859630546072907654, 28120785347777216299616324134973)
(-933956822375570319256506/625, 234792697653699949940877678308570853/15625)
(258904390351580092328338053814/242705241, 57203756105030165960928638637243015062200247/3781104949539)
(5022994028135485465036/9, 258991041991198186262714044200671/27)
(7311556630268996095109689449180816/11762684324329, 272462447398870689828352933727467450683054212093559/40342207885411711733)
(2820447267409586851553782693780486/3861449013249, 10426058403482737023933567344588727658578070528829/7587967413628040193)
(17403222196163686614696893651857206/33170193053449, 2109946934365832350562905560240245592532264175877009/191038983553732872293)
(-7774714078234245334456036435794/5644967689, 11555024045735674078027656633696319565697860001/424123357377637)
(373536598856905987012076460484914/10851654814225, 1041052274415313151193410307076439910453856789636017/35747358514197781625)
(-66727510750075408758523434/76729, 900657182034363260750093953300379194809/21253933)

Commentary

No commentary yet.