curve #3560

y² = x³ + x² − 20455520205827701656683702712846882718785x + 1117321581673616531309555089631503574135584564141219733283939

a-invariants: [0, 1, 0, -20455520205827701656683702712846882718785, 1117321581673616531309555089631503574135584564141219733283939]
rank (lower bound): ≥ 27
torsion subgroup: trivial
conductor (N): 447150730383917921426051671944550064682725516683851096390502869690505599723716416631723027726161758739752
discriminant (Δ): 8474748633768142725566279039220260724922260978390640711758753640679199715224562749436523395123920421215281425127999814912
Faltings height: 22.0269
naive height: 290.0708
primes of bad reduction: 2, 3, 7, 17, 29, 31, 53, 61, 317321, 223758923, 844098058598893011473765759, 898790071554039697918247235279344488957712631299957383
regulator: 183711703967819979223061518262.33740741078655236716685530364614343013604305451895934516567761
submitted by: FNacc
submitted at: 2026-09-28 14:09:19 UTC
last updated: 2026-09-28 14:09:19 UTC

Witness: 27 independent points log in to add more points →

(-255462109720345288034346/24025, -4300433234944353961210995137281264017/3723875)
(76125410097997761513, 35908373696825237807743499790)
(214326390214696419470583/2809, -4106055643022386082129332356835758/148877)
(390867767275097102763, 7268958795102310314297047064210)
(556160372374280202615, -12718850631000105163929578878458)
(8695954980305669269240155/2209, -25626723730872401673239513070137838066/103823)
(1031425198891510433895, 32822069440769901940978544929542)
(-21257319919612470909, 1241992550728947778301937343566)
(497151494841248905753359/25, -350527360581234700846861726780770798/125)
(14948047387846140263361/169, 7194628784922523062327607052214/2197)
(254403662702667941901/4, 2170380003375391100608770860979/8)
(4209836154203890677524511/42025, 2334760136986489063757546353795378434/8615125)
(128602558944003762542475/961, -26250552652759769716400434071468078/29791)
(818523121320431263206, 23081772204936430287859935456309)
(89591144496040746009, -61627851189356005751594667678)
(95039739742220324169, 178004687266441509170022872238)
(69006814168519294461019/729, 3363523140771945866965521733124822/19683)
(89025400437698908881, 42819003601766500590032762934)
(14952753595418284208079/169, 21400258686235973936512564421502/2197)
(10703674316160662472815/121, 8553818067500831927878078884402/1331)
(89462805514311804399, 57769289575534754815830662682)
(8742235910410102626804543/94249, 3881550648223726972992524875404038658/28934443)
(500576053205903350756798161/3385600, 7171020350872355425946012446280649123609/6229504000)
(737117877189602464640285449/8105409, 2211506172594219994445138407403831343982/23076099423)
(193728222329524117642047135/1666681, 1198190474357863339027266949365178631118/2151685171)
(111670069722271409151, 474974543420822773356281106534)
(56774216180819348763, 372795448357599207627199598610)

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