curve #1972

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y² + xy + y = x³ − x² − 154000135848065377643405687802x + 24206507105281303817046209683659227477580345

a-invariants

[1, -1, 1, -154000135848065377643405687802, 24206507105281303817046209683659227477580345]

rank (lower bound)

≥ 21

torsion subgroup

trivial

conductor (N)

83052206795666967948907407936121332539365862214957597382207520875013666

discriminant (Δ)

-19387039473922369469726235987002674572994802923079879959924373514337747546373707094294528

Faltings height

15.7031

naive height

213.3135

primes of bad reduction

2, 13, 17, 37, 41, 43, 38669, 1211806101859, 61472205471111997004333809722433989633255651773

regulator

106617881213168572790.87571179977590699096101561054615843496456565714698687936089

submitted by

Ritik Jain

submitted at

2026-09-25 20:07:20 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 20:09:16 UTC

Witness: 21 independent points log in to add more points →

(87104422125690445/81, -24201889316240073161831605/729)
(46559536295723583137243575417/107548452490249, 6936037571399013003087162286537666587970947/1115337356811919198693)
(272311278600697/9, -119456781756614464888067/27)
(178327413730161, -1554024469618252129593)
(1117628174751745, 35328640118597312549799)
(125034210607417, -2627917631093656048905)
(22177453939589721/25, -3025126811563563934392821/125)
(191248712434865, -1322613306090950290681)
(681717672391318297/2601, -180342547074063293911637395/132651)
(-726637361907238247/19881, -15299086822362255370893805741/2803221)
(6058748841151225/9, -405557461556086606148867/27)
(2142200509567609/9, 27483053566924755161597/27)
(554662220440257, -10460897996490303401433)
(3340133882216345305/9801, -3262344447277848919340158435/970299)
(-244112886107135, -6874079382626760942681)
(69031655931223617/289, 5034429807511504948700871/4913)
(428592978378481, -6077187586610676432953)
(167728770635772971758948495323090259726147/769779509563406160234274329, 21314179660847662904965602363869599232018187105620388789181891/21357455980353712079355664582652398436733)
(-25866873437103440867257528668911/58214343179061169, 31110541736207403587624220783582427745198380913/14045752215256290814433303)
(-2074363686194952900908659894311/24605376771942121, 23346849461236645383982126191837531340895208205/3859624276482757533544331)
(230971521898676059617963502801380443455373/949251932003928281953509769, 31238251724884279681208074546391665291915383915916780983250039/29246387817272989123593124402373216559397)

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