curve #1876

y² = x³ + x² − 125009015691897909842039213167821403072608420x + 532891803224022637629471819145629465159968904801598635012725052768

a-invariants: [0, 1, 0, -125009015691897909842039213167821403072608420, 532891803224022637629471819145629465159968904801598635012725052768]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 3786158254488676837311628156992254590861303672312593798120807724665750037995184059621892680
discriminant (Δ): 2350421882998039266233176064852947009058345463920609667701192071724234232263204611415105181913181840884704254652806034261418000800000
Faltings height: 24.2147
naive height: 316.2245
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 53, 79, 97, 1789, 119869, 4127325832889078913190920325976771316310319328001936071799241603
regulator: 1056506851828833468698017.2788817539121964556182046030441883817443471413316263267323435
submitted by: Ritik Jain
submitted at: 2026-09-25 17:27:44 UTC
last updated: 2026-09-25 17:27:44 UTC

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

(339427529200116537635975960883718233706583539963596/119737071267379748024289022801, -18589357844782903241061112237566813972558971463259254304990171449543961777680/41432672468968013853794727985746056643525799)
(-8830354666157447559232582077366/685549489, -1393690407001720983927287652588012277411693950/17949742270487)
(-11308252782996567236854644/1681, -71272866255067044047325039886007766240/68921)
(75726035049266399867809752/121, 658868859231138245801567838010303844520/1331)
(672997680179655809074314/169, 688567991372955833863386158023307850/2197)
(33240437499758400280339461/1156, 178881274564562623206071838353692283025/39304)
(-88048511958624727678286/225, 2574200899936672017118540717503317462/3375)
(35712098430829523265438, -6450901037501097606661872750823482)
(18762324280932262214930204/2209, -30064332553054305878461012659266500200/103823)
(39460970452987037339738586/3481, -155403875484579771438680804276394950550/205379)
(2010069300216022206026577/64, -2689220267499788058310392463594585479/512)
(18572949071329986414411, -2148936228807566386906544748483240)
(522627316030880040923196/121, -360912867825739146850397971047772440/1331)
(-487726416372513606415814/81, -753131532560316833399148867712656050/729)
(238342818441797488153806, -116234029728368599928778788266344150)
(1097107426774742681361256142613/5044516, -1147652351470103862843433055843473123902331737/11329982936)
(148388459874106164080201231966345751/12055763123881, -38794990587850169027806287182483384097082445390984730/41859309428715299221)
(-480352934767344925877355015156486307743278126237091/298514688049596246255428844004, 139339762405299254917416962924787680405878735117761072183773210807081715103965/163097970658738352140075562067912833849532008)
(3838823298021115997590769020796/242456041, 5996339810374434631878563863333358220019109400/3775283014411)
(-852174930792991062015743641086/199007449, 2792869402585851417230893630539035414486277570/2807398083043)
(-228212208411295090383497511461022993879592405971/29434185955124524120444804, 162542633407977511846621914735874193561421376474755138802703086671580005/159690118773833582301232518171887404408)
(-195035148242771216225560482/134689, 41676803591519513378881076625381606039270/49430863)
(-3170361450115837889153014/361, 6697295190793834458108142291225335690/6859)
(116517096263254139576671090287314803158/20616890863960561, 246045106506575063858122726761908104465525244276249815842/2960293407338085102411191)

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