curve #1851

y² + xy = x³ − 864462155097190812731820407329466910x + 309520540577003582194916832772576397653835845588220100

a-invariants: [1, 0, 0, -864462155097190812731820407329466910, 309520540577003582194916832772576397653835845588220100]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 861614133351910499431245932860954153102424934822093808035365057692096146870
discriminant (Δ): -42363232154625255844281687962158117953260733189773423913436729131356251078998617188040043451140300480000000
Faltings height: 19.4043
naive height: 259.8569
primes of bad reduction: 2, 3, 5, 11, 13, 17, 23, 47, 101, 113, 1500511, 638178113607283525870291450111320987270612576546074515273
regulator: 438217546118724877417.8134010707312080427009769810384628090114202321290211520519110
submitted by: Ritik Jain
submitted at: 2026-09-25 17:11:34 UTC
last updated: 2026-09-25 17:11:34 UTC

(785961827828855204460461633920805031844020/53907999502058927385889, -695407014799512585897600680991831783586487539005706788615780870/12516411228788926326358939757663537)
(43366754353296460780/81, -9268357074145226363958465230/729)
(4588367665920629037195/7396, -69657432288031531655155061490135/636056)
(1918024983821997372, -2389043510583811740879920718)
(176664758148875076235500/5329, -74225966660754778922815436632906830/389017)
(149246631022207873155/4, 1822733686066791383387572909695/8)
(4030003865396467020, 7891561950271721917191928290)
(12586497445489069155/4, -42891402365743783571593645305/8)
(1141639768499461656780/1849, 8396926491686995165629196197030/79507)
(-34048537821527076420/49, -260023960097808946553376610530/343)
(1986627170545794985620/361, -87357596840511425652204785212890/6859)
(885128402584674540, -487664236633576184594920110)
(914394227932252090380/1681, 1070709435565671750885494696130/68921)
(3343690915755906180, -5899355049159044634039959670)
(-290437218591065268, 732183752926773710324800482)
(-1058464412997258660, -196661205337163643559981230)
(815917468841859420, 383880733875159217639822290)
(143867922588927863148/289, 247946904496497582917773644066/4913)
(1395339937451529125853/2704, 4085674698202192033434244853931/140608)
(495555153695024316, 53176845166861796210490642)
(509577814804728420, 36491726558132029639477290)
(529884550489938420, 15334014100338298571059290)

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