curve #1857

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y² + xy = x³ − 217378645530923667721353487908449180x + 38438259774458690105462778714431491491319360290580752

a-invariants: [1, 0, 0, -217378645530923667721353487908449180, 38438259774458690105462778714431491491319360290580752]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 1576142395745699904568156597142527593194884801864256514653449350725833866327006330
discriminant (Δ): 19121456650389205622969015414309663920495057094537379221425190038209253543679812319160240971399824588800000
Faltings height: 19.1916
naive height: 255.7144
primes of bad reduction: 2, 3, 5, 17, 19, 29, 31, 37, 47, 53, 168991, 11616437356242962471450987207719439985289289452250876898964564819
regulator: 29284699022288547329584.4269393219188317555466741957661469034672859286743341173841338
submitted by: Ritik Jain
submitted at: 2026-09-25 17:14:22 UTC
last updated: 2026-09-25 17:14:22 UTC

Witness: 23 independent points log in to add more points →

(1061615778777249692280484353512127381698128619104/666376207923766422395220483601, 1051365188923874374397949032423119385944942628671110059943076974909660188/543975354846602434106391777436546261815585401)
(2259799204010764410717635126776/730038662929, 3360543068020119779095741505794504062814241276/623761824495784967)
(1256491921563084284344/1681, 37342831800086670797319606279428/68921)
(5697797525848067204728/121, 430070159171927899175962099533356/1331)
(36161346183994225236/169, -91162975148095175071777794984/2197)
(224256613543144588216/289, -2852081734676477860264718769436/4913)
(53885981880177584056/225, -36060372879798893595114445924/3375)
(-528729560385538478, 74590956084163295163415408)
(73701682702578597364/19881, 543799278073661028106437517400888/2803221)
(-779773514587234072136/3481, 56578921030396150635600183917612/205379)
(-5704157302274941666613/11236, 159590859724649737560104792762863/1191016)
(640139967155291464, -401996928195819357509641052)
(-52188710108335000496/121, -303396207418962874092461268892/1331)
(494660515370539948876/729, 8876071460010832165816004914624/19683)
(103661541845838241144, 1055412202122490735471692136228)
(7905607238775703229352568/1261129, -22168299177399825712972617447297784244/1416247867)
(610693494086924515774064315893816/3545014338840529, 16489315490881671926405955196188278946814686439036/211070235269894889992167)
(8413489979420258829688/34969, 52705065255290945241678216213100/6539203)
(215510950235081984176/729, 67068214513577852220473768324/19683)
(24055770553280990458756966/101143249, 14061254326616402060522659376308669024/1017197655193)
(237303383909414584, 14724550210319006218035748)
(926137704768665551/4, 182386216878367664202131549/8)
(8369976883113585583864/36481, 176496628116313276214144315426588/6967871)

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